diff --git "a/cube2/test.jsonl" "b/cube2/test.jsonl" new file mode 100644--- /dev/null +++ "b/cube2/test.jsonl" @@ -0,0 +1,502 @@ +{"taskType": "roll_to_target_top_face", "code": "C001", "name": "Goal Roll C001", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "smile", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "5", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "triangle", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "smile", "rotation": 90}, "BACK": {"patternId": "5", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "triangle", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "5", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C001/initial_net.png", "targetTopFaceImage": "../images/C001/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 1, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-001.json"}, "rollSequence": ["N", "E", "S"], "observedPathFaces": [{"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "smile", "rotation": 90}, "BACK": {"patternId": "5", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "triangle", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C001\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=5, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=5, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=smile, rotation=90]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=triangle, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=5, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=smile, rotation=90\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=triangle, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C001/initial_net.png", "targetTopFaceImage": "images/C001/target_top_face.png"}, "__sample_id__": "C001"} +{"taskType": "roll_to_target_top_face", "code": "C002", "name": "Goal Roll C002", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "diamond", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "M", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "diamond", "rotation": 180}, "RIGHT": {"patternId": "M", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "diamond", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C002/initial_net.png", "targetTopFaceImage": "../images/C002/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 2, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-002.json"}, "rollSequence": ["S", "E"], "observedPathFaces": [{"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "diamond", "rotation": 180}, "RIGHT": {"patternId": "M", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C002\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=diamond, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=M, rotation=180]\n [FRONT: patternId=diamond, rotation=180]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=M, rotation=180\n- FRONT: patternId=diamond, rotation=180\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C002/initial_net.png", "targetTopFaceImage": "images/C002/target_top_face.png"}, "__sample_id__": "C002"} +{"taskType": "roll_to_target_top_face", "code": "C003", "name": "Goal Roll C003", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "heart", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_left", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 0}, "RIGHT": {"patternId": "arrow_left", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "heart", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C003/initial_net.png", "targetTopFaceImage": "../images/C003/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 3, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-003.json"}, "rollSequence": ["S", "E", "W"], "observedPathFaces": [{"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 0}, "RIGHT": {"patternId": "arrow_left", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C003\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=heart, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=arrow_left, rotation=270]\n [FRONT: patternId=heart, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=arrow_left, rotation=270\n- FRONT: patternId=heart, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C003/initial_net.png", "targetTopFaceImage": "images/C003/target_top_face.png"}, "__sample_id__": "C003"} +{"taskType": "roll_to_target_top_face", "code": "C004", "name": "Goal Roll C004", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "square", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "E", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "E", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "E", "rotation": 90}, "LEFT": {"patternId": "E", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "E", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C004/initial_net.png", "targetTopFaceImage": "../images/C004/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 4, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-004.json"}, "rollSequence": ["S", "W", "W"], "observedPathFaces": [{"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "E", "rotation": 90}, "LEFT": {"patternId": "E", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C004\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=E, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=E, rotation=90]\n[LEFT: patternId=E, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=square, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=E, rotation=90\n- LEFT: patternId=E, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=square, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C004/initial_net.png", "targetTopFaceImage": "images/C004/target_top_face.png"}, "__sample_id__": "C004"} +{"taskType": "roll_to_target_top_face", "code": "C005", "name": "Goal Roll C005", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "M", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_left", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "arrow_left", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "M", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C005/initial_net.png", "targetTopFaceImage": "../images/C005/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 5, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-005.json"}, "rollSequence": ["W", "N"], "observedPathFaces": [{"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "arrow_left", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C005\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=M, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=M, rotation=0]\n[LEFT: patternId=arrow_left, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=M, rotation=0\n- LEFT: patternId=arrow_left, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C005/initial_net.png", "targetTopFaceImage": "images/C005/target_top_face.png"}, "__sample_id__": "C005"} +{"taskType": "roll_to_target_top_face", "code": "C006", "name": "Goal Roll C006", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "star", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "R", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "star", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "R", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "R", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C006/initial_net.png", "targetTopFaceImage": "../images/C006/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 6, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-006.json"}, "rollSequence": ["E", "E"], "observedPathFaces": [{"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E"]}, "legacy_answer": {"TOP": {"patternId": "star", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "R", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C006\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=R, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=star, rotation=180] [RIGHT: patternId=R, rotation=270]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=star, rotation=180\n- RIGHT: patternId=R, rotation=270\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C006/initial_net.png", "targetTopFaceImage": "images/C006/target_top_face.png"}, "__sample_id__": "C006"} +{"taskType": "roll_to_target_top_face", "code": "C007", "name": "Goal Roll C007", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "I", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "7", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "Z", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "I", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "7", "rotation": 180}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "Z", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C007/initial_net.png", "targetTopFaceImage": "../images/C007/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 7, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-007.json"}, "rollSequence": ["N", "N", "E"], "observedPathFaces": [{"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "I", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "7", "rotation": 180}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C007\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=Z, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=Z, rotation=90]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=I, rotation=0] [RIGHT: patternId=7, rotation=180]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Z, rotation=90\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=I, rotation=0\n- RIGHT: patternId=7, rotation=180\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C007/initial_net.png", "targetTopFaceImage": "images/C007/target_top_face.png"}, "__sample_id__": "C007"} +{"taskType": "roll_to_target_top_face", "code": "C008", "name": "Goal Roll C008", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "O", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "I", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "N", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "O", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 180}, "LEFT": {"patternId": "N", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "I", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C008/initial_net.png", "targetTopFaceImage": "../images/C008/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 8, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-008.json"}, "rollSequence": ["N", "N", "W"], "observedPathFaces": [{"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 180}, "LEFT": {"patternId": "N", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C008\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=I, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=I, rotation=180]\n[LEFT: patternId=N, rotation=0] [TOP: patternId=O, rotation=270] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=I, rotation=180\n- LEFT: patternId=N, rotation=0\n- TOP: patternId=O, rotation=270\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C008/initial_net.png", "targetTopFaceImage": "images/C008/target_top_face.png"}, "__sample_id__": "C008"} +{"taskType": "roll_to_target_top_face", "code": "C009", "name": "Goal Roll C009", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "A", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "Z", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "heart", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "A", "rotation": 270}, "BACK": {"patternId": "Z", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "heart", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "Z", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C009/initial_net.png", "targetTopFaceImage": "../images/C009/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 9, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-009.json"}, "rollSequence": ["E", "W", "N"], "observedPathFaces": [{"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "A", "rotation": 270}, "BACK": {"patternId": "Z", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "heart", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C009\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=Z, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=Z, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=A, rotation=270]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=heart, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Z, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=A, rotation=270\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=heart, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C009/initial_net.png", "targetTopFaceImage": "images/C009/target_top_face.png"}, "__sample_id__": "C009"} +{"taskType": "roll_to_target_top_face", "code": "C010", "name": "Goal Roll C010", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "T", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "2", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "T", "rotation": 90}, "LEFT": {"patternId": "2", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "T", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C010/initial_net.png", "targetTopFaceImage": "../images/C010/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 10, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-010.json"}, "rollSequence": ["N", "W"], "observedPathFaces": [{"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "T", "rotation": 90}, "LEFT": {"patternId": "2", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C010\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=T, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=T, rotation=90]\n[LEFT: patternId=2, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=T, rotation=90\n- LEFT: patternId=2, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C010/initial_net.png", "targetTopFaceImage": "images/C010/target_top_face.png"}, "__sample_id__": "C010"} +{"taskType": "roll_to_target_top_face", "code": "C011", "name": "Goal Roll C011", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "H", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "plus", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "plus", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "H", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C011/initial_net.png", "targetTopFaceImage": "../images/C011/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 11, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-011.json"}, "rollSequence": ["S", "W"], "observedPathFaces": [{"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "plus", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C011\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=H, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=plus, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=H, rotation=180]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=plus, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=H, rotation=180\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C011/initial_net.png", "targetTopFaceImage": "images/C011/target_top_face.png"}, "__sample_id__": "C011"} +{"taskType": "roll_to_target_top_face", "code": "C012", "name": "Goal Roll C012", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "2", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "plus", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "plus", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "2", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C012/initial_net.png", "targetTopFaceImage": "../images/C012/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 12, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-012.json"}, "rollSequence": ["S", "N"], "observedPathFaces": [{"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "plus", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C012\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=2, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=2, rotation=270]\n [BOTTOM: patternId=plus, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=2, rotation=270\n- BOTTOM: patternId=plus, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C012/initial_net.png", "targetTopFaceImage": "images/C012/target_top_face.png"}, "__sample_id__": "C012"} +{"taskType": "roll_to_target_top_face", "code": "C013", "name": "Goal Roll C013", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "W", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "W", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "R", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "W", "rotation": 270}, "FRONT": {"patternId": "W", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "R", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "W", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C013/initial_net.png", "targetTopFaceImage": "../images/C013/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 13, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-013.json"}, "rollSequence": ["W", "S", "W"], "observedPathFaces": [{"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "W", "rotation": 270}, "FRONT": {"patternId": "W", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "R", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C013\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=W, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=R, rotation=0] [TOP: patternId=W, rotation=270] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=W, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=R, rotation=0\n- TOP: patternId=W, rotation=270\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=W, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C013/initial_net.png", "targetTopFaceImage": "images/C013/target_top_face.png"}, "__sample_id__": "C013"} +{"taskType": "roll_to_target_top_face", "code": "C014", "name": "Goal Roll C014", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_left", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "Y", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_left", "rotation": 180}, "BACK": {"patternId": "Y", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "Y", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C014/initial_net.png", "targetTopFaceImage": "../images/C014/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 14, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-014.json"}, "rollSequence": ["E", "N"], "observedPathFaces": [{"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_left", "rotation": 180}, "BACK": {"patternId": "Y", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C014\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=Y, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=Y, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=arrow_left, rotation=180]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Y, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=arrow_left, rotation=180\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C014/initial_net.png", "targetTopFaceImage": "images/C014/target_top_face.png"}, "__sample_id__": "C014"} +{"taskType": "roll_to_target_top_face", "code": "C015", "name": "Goal Roll C015", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "4", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "6", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "O", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "4", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "6", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "O", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "4", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C015/initial_net.png", "targetTopFaceImage": "../images/C015/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 3, "targetRotationOffset": 270, "levelId": 15, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-015.json"}, "rollSequence": ["S", "N", "N"], "observedPathFaces": [{"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "4", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "6", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "O", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C015\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=4, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=6, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=4, rotation=90]\n [BOTTOM: patternId=O, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=6, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=4, rotation=90\n- BOTTOM: patternId=O, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C015/initial_net.png", "targetTopFaceImage": "images/C015/target_top_face.png"}, "__sample_id__": "C015"} +{"taskType": "roll_to_target_top_face", "code": "C016", "name": "Goal Roll C016", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "H", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_left", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_left", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "H", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C016/initial_net.png", "targetTopFaceImage": "../images/C016/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 16, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-016.json"}, "rollSequence": ["S", "W"], "observedPathFaces": [{"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_left", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C016\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=H, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=arrow_left, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=H, rotation=180]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=arrow_left, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=H, rotation=180\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C016/initial_net.png", "targetTopFaceImage": "images/C016/target_top_face.png"}, "__sample_id__": "C016"} +{"taskType": "roll_to_target_top_face", "code": "C017", "name": "Goal Roll C017", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "M", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "T", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "J", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "M", "rotation": 0}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "J", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "T", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C017/initial_net.png", "targetTopFaceImage": "../images/C017/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 17, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-017.json"}, "rollSequence": ["E", "N", "W"], "observedPathFaces": [{"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "M", "rotation": 0}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "J", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C017\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=T, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=T, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=M, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=J, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=T, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=M, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=J, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C017/initial_net.png", "targetTopFaceImage": "images/C017/target_top_face.png"}, "__sample_id__": "C017"} +{"taskType": "roll_to_target_top_face", "code": "C018", "name": "Goal Roll C018", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "smile", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "9", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "4", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "smile", "rotation": 180}, "LEFT": {"patternId": "9", "rotation": 180}, "BOTTOM": {"patternId": "4", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "smile", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C018/initial_net.png", "targetTopFaceImage": "../images/C018/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 18, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-018.json"}, "rollSequence": ["N", "W", "S"], "observedPathFaces": [{"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "smile", "rotation": 180}, "LEFT": {"patternId": "9", "rotation": 180}, "BOTTOM": {"patternId": "4", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C018\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=smile, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=smile, rotation=180]\n[LEFT: patternId=9, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=4, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=smile, rotation=180\n- LEFT: patternId=9, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=4, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C018/initial_net.png", "targetTopFaceImage": "images/C018/target_top_face.png"}, "__sample_id__": "C018"} +{"taskType": "roll_to_target_top_face", "code": "C019", "name": "Goal Roll C019", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "8", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "H", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "8", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "H", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "H", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C019/initial_net.png", "targetTopFaceImage": "../images/C019/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 19, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-019.json"}, "rollSequence": ["E", "E"], "observedPathFaces": [{"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E"]}, "legacy_answer": {"TOP": {"patternId": "8", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "H", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C019\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=H, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=8, rotation=90] [RIGHT: patternId=H, rotation=270]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=8, rotation=90\n- RIGHT: patternId=H, rotation=270\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C019/initial_net.png", "targetTopFaceImage": "images/C019/target_top_face.png"}, "__sample_id__": "C019"} +{"taskType": "roll_to_target_top_face", "code": "C020", "name": "Goal Roll C020", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "9", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "A", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "9", "rotation": 90}, "LEFT": {"patternId": "A", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "9", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C020/initial_net.png", "targetTopFaceImage": "../images/C020/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 20, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-020.json"}, "rollSequence": ["W", "N"], "observedPathFaces": [{"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "9", "rotation": 90}, "LEFT": {"patternId": "A", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C020\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=9, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=9, rotation=90]\n[LEFT: patternId=A, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=9, rotation=90\n- LEFT: patternId=A, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C020/initial_net.png", "targetTopFaceImage": "images/C020/target_top_face.png"}, "__sample_id__": "C020"} +{"taskType": "roll_to_target_top_face", "code": "C021", "name": "Goal Roll C021", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "N", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "V", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "4", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "N", "rotation": 90}, "BACK": {"patternId": "V", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "4", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "V", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C021/initial_net.png", "targetTopFaceImage": "../images/C021/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 21, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-021.json"}, "rollSequence": ["N", "S", "E"], "observedPathFaces": [{"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "N", "rotation": 90}, "BACK": {"patternId": "V", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "4", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C021\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=V, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=V, rotation=270]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=N, rotation=90]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=4, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=V, rotation=270\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=N, rotation=90\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=4, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C021/initial_net.png", "targetTopFaceImage": "images/C021/target_top_face.png"}, "__sample_id__": "C021"} +{"taskType": "roll_to_target_top_face", "code": "C022", "name": "Goal Roll C022", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "W", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "I", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "W", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "W", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "I", "rotation": 180}, "BOTTOM": {"patternId": "W", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "W", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C022/initial_net.png", "targetTopFaceImage": "../images/C022/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 22, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-022.json"}, "rollSequence": ["W", "E", "S"], "observedPathFaces": [{"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "W", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "I", "rotation": 180}, "BOTTOM": {"patternId": "W", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C022\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=W, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=I, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=W, rotation=180]\n [BOTTOM: patternId=W, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=I, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=W, rotation=180\n- BOTTOM: patternId=W, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C022/initial_net.png", "targetTopFaceImage": "images/C022/target_top_face.png"}, "__sample_id__": "C022"} +{"taskType": "roll_to_target_top_face", "code": "C023", "name": "Goal Roll C023", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "C", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "G", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "C", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "G", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "G", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C023/initial_net.png", "targetTopFaceImage": "../images/C023/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 23, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-023.json"}, "rollSequence": ["N", "N"], "observedPathFaces": [{"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N"]}, "legacy_answer": {"TOP": {"patternId": "C", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "G", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C023\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=G, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=G, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=C, rotation=90] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=G, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=C, rotation=90\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C023/initial_net.png", "targetTopFaceImage": "images/C023/target_top_face.png"}, "__sample_id__": "C023"} +{"taskType": "roll_to_target_top_face", "code": "C024", "name": "Goal Roll C024", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "1", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "3", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "1", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "1", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C024/initial_net.png", "targetTopFaceImage": "../images/C024/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 24, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-024.json"}, "rollSequence": ["S", "W"], "observedPathFaces": [{"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "1", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C024\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=1, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=3, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=1, rotation=180]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=3, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=1, rotation=180\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C024/initial_net.png", "targetTopFaceImage": "images/C024/target_top_face.png"}, "__sample_id__": "C024"} +{"taskType": "roll_to_target_top_face", "code": "C025", "name": "Goal Roll C025", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_right", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_down", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 0}, "BACK": {"patternId": "arrow_down", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "arrow_down", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C025/initial_net.png", "targetTopFaceImage": "../images/C025/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 25, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-025.json"}, "rollSequence": ["N", "E"], "observedPathFaces": [{"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 0}, "BACK": {"patternId": "arrow_down", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C025\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=arrow_down, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_down, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=arrow_right, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_down, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=arrow_right, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C025/initial_net.png", "targetTopFaceImage": "images/C025/target_top_face.png"}, "__sample_id__": "C025"} +{"taskType": "roll_to_target_top_face", "code": "C026", "name": "Goal Roll C026", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "D", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "K", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "R", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 270}, "RIGHT": {"patternId": "K", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "R", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "R", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C026/initial_net.png", "targetTopFaceImage": "../images/C026/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 3, "targetRotationOffset": 180, "levelId": 26, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-026.json"}, "rollSequence": ["W", "S", "S"], "observedPathFaces": [{"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 270}, "RIGHT": {"patternId": "K", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "R", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C026\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=R, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=R, rotation=90] [TOP: patternId=?, rotation=0] [RIGHT: patternId=K, rotation=90]\n [FRONT: patternId=D, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=R, rotation=90\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=K, rotation=90\n- FRONT: patternId=D, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C026/initial_net.png", "targetTopFaceImage": "images/C026/target_top_face.png"}, "__sample_id__": "C026"} +{"taskType": "roll_to_target_top_face", "code": "C027", "name": "Goal Roll C027", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "P", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "8", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "P", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "P", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C027/initial_net.png", "targetTopFaceImage": "../images/C027/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 27, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-027.json"}, "rollSequence": ["N", "S", "N"], "observedPathFaces": [{"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "S", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "P", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C027\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=P, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=P, rotation=90]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=8, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=P, rotation=90\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=8, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C027/initial_net.png", "targetTopFaceImage": "images/C027/target_top_face.png"}, "__sample_id__": "C027"} +{"taskType": "roll_to_target_top_face", "code": "C028", "name": "Goal Roll C028", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "circle", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "star", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "circle", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "star", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "circle", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C028/initial_net.png", "targetTopFaceImage": "../images/C028/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 28, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-028.json"}, "rollSequence": ["S", "N"], "observedPathFaces": [{"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "circle", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "star", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C028\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=circle, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=circle, rotation=270]\n [BOTTOM: patternId=star, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=circle, rotation=270\n- BOTTOM: patternId=star, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C028/initial_net.png", "targetTopFaceImage": "images/C028/target_top_face.png"}, "__sample_id__": "C028"} +{"taskType": "roll_to_target_top_face", "code": "C029", "name": "Goal Roll C029", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "P", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "A", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "P", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "A", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "P", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C029/initial_net.png", "targetTopFaceImage": "../images/C029/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 29, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-029.json"}, "rollSequence": ["W", "S", "N"], "observedPathFaces": [{"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "P", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "A", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C029\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=P, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=A, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=P, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=A, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=P, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C029/initial_net.png", "targetTopFaceImage": "images/C029/target_top_face.png"}, "__sample_id__": "C029"} +{"taskType": "roll_to_target_top_face", "code": "C030", "name": "Goal Roll C030", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "N", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "H", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "R", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "H", "rotation": 90}, "LEFT": {"patternId": "R", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "H", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C030/initial_net.png", "targetTopFaceImage": "../images/C030/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 3, "targetRotationOffset": 180, "levelId": 30, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-030.json"}, "rollSequence": ["N", "W", "W"], "observedPathFaces": [{"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "H", "rotation": 90}, "LEFT": {"patternId": "R", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C030\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=H, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=H, rotation=90]\n[LEFT: patternId=R, rotation=90] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=N, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=H, rotation=90\n- LEFT: patternId=R, rotation=90\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=N, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C030/initial_net.png", "targetTopFaceImage": "images/C030/target_top_face.png"}, "__sample_id__": "C030"} +{"taskType": "roll_to_target_top_face", "code": "C031", "name": "Goal Roll C031", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "T", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "G", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "T", "rotation": 270}, "LEFT": {"patternId": "G", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "T", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C031/initial_net.png", "targetTopFaceImage": "../images/C031/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 31, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-031.json"}, "rollSequence": ["W", "N"], "observedPathFaces": [{"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "T", "rotation": 270}, "LEFT": {"patternId": "G", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C031\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=T, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=T, rotation=270]\n[LEFT: patternId=G, rotation=90] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=T, rotation=270\n- LEFT: patternId=G, rotation=90\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C031/initial_net.png", "targetTopFaceImage": "images/C031/target_top_face.png"}, "__sample_id__": "C031"} +{"taskType": "roll_to_target_top_face", "code": "C032", "name": "Goal Roll C032", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "9", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "6", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "9", "rotation": 90}, "FRONT": {"patternId": "6", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "6", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C032/initial_net.png", "targetTopFaceImage": "../images/C032/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 32, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-032.json"}, "rollSequence": ["S", "S", "N"], "observedPathFaces": [{"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "N"]}, "legacy_answer": {"TOP": {"patternId": "9", "rotation": 90}, "FRONT": {"patternId": "6", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C032\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=6, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=9, rotation=90] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=6, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=9, rotation=90\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=6, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C032/initial_net.png", "targetTopFaceImage": "images/C032/target_top_face.png"}, "__sample_id__": "C032"} +{"taskType": "roll_to_target_top_face", "code": "C033", "name": "Goal Roll C033", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "5", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "K", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "I", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "5", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "I", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "K", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C033/initial_net.png", "targetTopFaceImage": "../images/C033/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 33, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-033.json"}, "rollSequence": ["N", "W", "N"], "observedPathFaces": [{"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "5", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "I", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C033\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=K, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=K, rotation=270]\n[LEFT: patternId=I, rotation=90] [TOP: patternId=5, rotation=270] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=K, rotation=270\n- LEFT: patternId=I, rotation=90\n- TOP: patternId=5, rotation=270\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C033/initial_net.png", "targetTopFaceImage": "images/C033/target_top_face.png"}, "__sample_id__": "C033"} +{"taskType": "roll_to_target_top_face", "code": "C034", "name": "Goal Roll C034", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "U", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "H", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "U", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "H", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "H", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C034/initial_net.png", "targetTopFaceImage": "../images/C034/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 34, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-034.json"}, "rollSequence": ["W", "W"], "observedPathFaces": [{"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W"]}, "legacy_answer": {"TOP": {"patternId": "U", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "H", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C034\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=H, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=H, rotation=0] [TOP: patternId=U, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=H, rotation=0\n- TOP: patternId=U, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C034/initial_net.png", "targetTopFaceImage": "images/C034/target_top_face.png"}, "__sample_id__": "C034"} +{"taskType": "roll_to_target_top_face", "code": "C035", "name": "Goal Roll C035", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "arrow_left", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "Z", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "arrow_left", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "Z", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "arrow_left", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C035/initial_net.png", "targetTopFaceImage": "../images/C035/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 35, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-035.json"}, "rollSequence": ["W", "S"], "observedPathFaces": [{"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "arrow_left", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "Z", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C035\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=arrow_left, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=Z, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=arrow_left, rotation=180]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=Z, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=arrow_left, rotation=180\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C035/initial_net.png", "targetTopFaceImage": "images/C035/target_top_face.png"}, "__sample_id__": "C035"} +{"taskType": "roll_to_target_top_face", "code": "C036", "name": "Goal Roll C036", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_up", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "circle", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_up", "rotation": 90}, "LEFT": {"patternId": "circle", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "arrow_up", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C036/initial_net.png", "targetTopFaceImage": "../images/C036/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 36, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-036.json"}, "rollSequence": ["W", "N", "S"], "observedPathFaces": [{"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_up", "rotation": 90}, "LEFT": {"patternId": "circle", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C036\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=arrow_up, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_up, rotation=90]\n[LEFT: patternId=circle, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_up, rotation=90\n- LEFT: patternId=circle, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C036/initial_net.png", "targetTopFaceImage": "images/C036/target_top_face.png"}, "__sample_id__": "C036"} +{"taskType": "roll_to_target_top_face", "code": "C037", "name": "Goal Roll C037", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "H", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "2", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "H", "rotation": 270}, "LEFT": {"patternId": "2", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "H", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C037/initial_net.png", "targetTopFaceImage": "../images/C037/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 37, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-037.json"}, "rollSequence": ["N", "W"], "observedPathFaces": [{"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "H", "rotation": 270}, "LEFT": {"patternId": "2", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C037\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=H, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=H, rotation=270]\n[LEFT: patternId=2, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=H, rotation=270\n- LEFT: patternId=2, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C037/initial_net.png", "targetTopFaceImage": "images/C037/target_top_face.png"}, "__sample_id__": "C037"} +{"taskType": "roll_to_target_top_face", "code": "C038", "name": "Goal Roll C038", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "P", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "Q", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "P", "rotation": 270}, "BACK": {"patternId": "Q", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "Q", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C038/initial_net.png", "targetTopFaceImage": "../images/C038/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 38, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-038.json"}, "rollSequence": ["N", "E"], "observedPathFaces": [{"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "P", "rotation": 270}, "BACK": {"patternId": "Q", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C038\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=Q, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=Q, rotation=270]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=P, rotation=270]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Q, rotation=270\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=P, rotation=270\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C038/initial_net.png", "targetTopFaceImage": "images/C038/target_top_face.png"}, "__sample_id__": "C038"} +{"taskType": "roll_to_target_top_face", "code": "C039", "name": "Goal Roll C039", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "B", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "I", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 0}, "LEFT": {"patternId": "I", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "B", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C039/initial_net.png", "targetTopFaceImage": "../images/C039/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 39, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-039.json"}, "rollSequence": ["W", "N"], "observedPathFaces": [{"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 0}, "LEFT": {"patternId": "I", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C039\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=B, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=B, rotation=0]\n[LEFT: patternId=I, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=B, rotation=0\n- LEFT: patternId=I, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C039/initial_net.png", "targetTopFaceImage": "images/C039/target_top_face.png"}, "__sample_id__": "C039"} +{"taskType": "roll_to_target_top_face", "code": "C040", "name": "Goal Roll C040", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "I", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "smile", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 0}, "LEFT": {"patternId": "smile", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "I", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C040/initial_net.png", "targetTopFaceImage": "../images/C040/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 40, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-040.json"}, "rollSequence": ["N", "W"], "observedPathFaces": [{"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 0}, "LEFT": {"patternId": "smile", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C040\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=I, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=I, rotation=0]\n[LEFT: patternId=smile, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=I, rotation=0\n- LEFT: patternId=smile, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C040/initial_net.png", "targetTopFaceImage": "images/C040/target_top_face.png"}, "__sample_id__": "C040"} +{"taskType": "roll_to_target_top_face", "code": "C041", "name": "Goal Roll C041", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "star", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "6", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "star", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "star", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C041/initial_net.png", "targetTopFaceImage": "../images/C041/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 41, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-041.json"}, "rollSequence": ["E", "S"], "observedPathFaces": [{"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "star", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C041\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=star, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=6, rotation=180]\n [FRONT: patternId=star, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=6, rotation=180\n- FRONT: patternId=star, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C041/initial_net.png", "targetTopFaceImage": "images/C041/target_top_face.png"}, "__sample_id__": "C041"} +{"taskType": "roll_to_target_top_face", "code": "C042", "name": "Goal Roll C042", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "arrow_left", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "star", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "arrow_left", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "star", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "arrow_left", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C042/initial_net.png", "targetTopFaceImage": "../images/C042/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 42, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-042.json"}, "rollSequence": ["S", "W"], "observedPathFaces": [{"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "arrow_left", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "star", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C042\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=arrow_left, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=star, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=arrow_left, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=star, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=arrow_left, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C042/initial_net.png", "targetTopFaceImage": "images/C042/target_top_face.png"}, "__sample_id__": "C042"} +{"taskType": "roll_to_target_top_face", "code": "C043", "name": "Goal Roll C043", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "S", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "P", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 0}, "BACK": {"patternId": "P", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "P", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C043/initial_net.png", "targetTopFaceImage": "../images/C043/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 43, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-043.json"}, "rollSequence": ["N", "E"], "observedPathFaces": [{"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 0}, "BACK": {"patternId": "P", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C043\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=P, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=P, rotation=270]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=S, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=P, rotation=270\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=S, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C043/initial_net.png", "targetTopFaceImage": "images/C043/target_top_face.png"}, "__sample_id__": "C043"} +{"taskType": "roll_to_target_top_face", "code": "C044", "name": "Goal Roll C044", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "heart", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "7", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "smile", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "heart", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "7", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "smile", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "smile", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C044/initial_net.png", "targetTopFaceImage": "../images/C044/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 3, "targetRotationOffset": 90, "levelId": 44, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-044.json"}, "rollSequence": ["W", "W", "W"], "observedPathFaces": [{"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "heart", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "7", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "smile", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C044\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=smile, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=smile, rotation=0] [TOP: patternId=heart, rotation=0] [RIGHT: patternId=7, rotation=180]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=smile, rotation=0\n- TOP: patternId=heart, rotation=0\n- RIGHT: patternId=7, rotation=180\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C044/initial_net.png", "targetTopFaceImage": "images/C044/target_top_face.png"}, "__sample_id__": "C044"} +{"taskType": "roll_to_target_top_face", "code": "C045", "name": "Goal Roll C045", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "circle", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "U", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "D", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "circle", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "U", "rotation": 90}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "D", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C045/initial_net.png", "targetTopFaceImage": "../images/C045/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 45, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-045.json"}, "rollSequence": ["E", "N", "E"], "observedPathFaces": [{"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "circle", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "U", "rotation": 90}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C045\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=D, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=D, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=circle, rotation=270] [RIGHT: patternId=U, rotation=90]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=D, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=circle, rotation=270\n- RIGHT: patternId=U, rotation=90\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C045/initial_net.png", "targetTopFaceImage": "images/C045/target_top_face.png"}, "__sample_id__": "C045"} +{"taskType": "roll_to_target_top_face", "code": "C046", "name": "Goal Roll C046", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "arrow_left", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "C", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "arrow_left", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "C", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "C", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C046/initial_net.png", "targetTopFaceImage": "../images/C046/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 46, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-046.json"}, "rollSequence": ["W", "W", "E"], "observedPathFaces": [{"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "E"]}, "legacy_answer": {"TOP": {"patternId": "arrow_left", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "C", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C046\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=C, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=C, rotation=180] [TOP: patternId=arrow_left, rotation=90] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=C, rotation=180\n- TOP: patternId=arrow_left, rotation=90\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C046/initial_net.png", "targetTopFaceImage": "images/C046/target_top_face.png"}, "__sample_id__": "C046"} +{"taskType": "roll_to_target_top_face", "code": "C047", "name": "Goal Roll C047", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "N", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_up", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "H", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "N", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_up", "rotation": 90}, "LEFT": {"patternId": "H", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "arrow_up", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C047/initial_net.png", "targetTopFaceImage": "../images/C047/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 47, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-047.json"}, "rollSequence": ["W", "W", "N"], "observedPathFaces": [{"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "N", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_up", "rotation": 90}, "LEFT": {"patternId": "H", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C047\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=arrow_up, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_up, rotation=90]\n[LEFT: patternId=H, rotation=180] [TOP: patternId=N, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_up, rotation=90\n- LEFT: patternId=H, rotation=180\n- TOP: patternId=N, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C047/initial_net.png", "targetTopFaceImage": "images/C047/target_top_face.png"}, "__sample_id__": "C047"} +{"taskType": "roll_to_target_top_face", "code": "C048", "name": "Goal Roll C048", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "smile", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "plus", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "A", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "smile", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "plus", "rotation": 270}, "LEFT": {"patternId": "A", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "smile", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C048/initial_net.png", "targetTopFaceImage": "../images/C048/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 3, "targetRotationOffset": 180, "levelId": 48, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-048.json"}, "rollSequence": ["S", "W", "W"], "observedPathFaces": [{"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "smile", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "plus", "rotation": 270}, "LEFT": {"patternId": "A", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C048\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=smile, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=plus, rotation=270]\n[LEFT: patternId=A, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=smile, rotation=180]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=plus, rotation=270\n- LEFT: patternId=A, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=smile, rotation=180\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C048/initial_net.png", "targetTopFaceImage": "images/C048/target_top_face.png"}, "__sample_id__": "C048"} +{"taskType": "roll_to_target_top_face", "code": "C049", "name": "Goal Roll C049", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "V", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "D", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Y", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "V", "rotation": 180}, "FRONT": {"patternId": "D", "rotation": 0}, "RIGHT": {"patternId": "Y", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "D", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C049/initial_net.png", "targetTopFaceImage": "../images/C049/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 49, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-049.json"}, "rollSequence": ["S", "S", "E"], "observedPathFaces": [{"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "V", "rotation": 180}, "FRONT": {"patternId": "D", "rotation": 0}, "RIGHT": {"patternId": "Y", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C049\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=D, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=V, rotation=180] [RIGHT: patternId=Y, rotation=180]\n [FRONT: patternId=D, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=V, rotation=180\n- RIGHT: patternId=Y, rotation=180\n- FRONT: patternId=D, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C049/initial_net.png", "targetTopFaceImage": "images/C049/target_top_face.png"}, "__sample_id__": "C049"} +{"taskType": "roll_to_target_top_face", "code": "C050", "name": "Goal Roll C050", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "3", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "P", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "8", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "3", "rotation": 180}, "LEFT": {"patternId": "P", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "3", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C050/initial_net.png", "targetTopFaceImage": "../images/C050/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 50, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-050.json"}, "rollSequence": ["W", "E", "N"], "observedPathFaces": [{"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "3", "rotation": 180}, "LEFT": {"patternId": "P", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C050\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=3, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=3, rotation=180]\n[LEFT: patternId=P, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=8, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=3, rotation=180\n- LEFT: patternId=P, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=8, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C050/initial_net.png", "targetTopFaceImage": "images/C050/target_top_face.png"}, "__sample_id__": "C050"} +{"taskType": "roll_to_target_top_face", "code": "C051", "name": "Goal Roll C051", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "6", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "L", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "star", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "6", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "L", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "star", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "L", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C051/initial_net.png", "targetTopFaceImage": "../images/C051/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 51, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-051.json"}, "rollSequence": ["W", "W", "W"], "observedPathFaces": [{"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "6", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "L", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "star", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C051\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=L, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=star, rotation=270] [TOP: patternId=6, rotation=0] [RIGHT: patternId=L, rotation=90]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=star, rotation=270\n- TOP: patternId=6, rotation=0\n- RIGHT: patternId=L, rotation=90\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C051/initial_net.png", "targetTopFaceImage": "images/C051/target_top_face.png"}, "__sample_id__": "C051"} +{"taskType": "roll_to_target_top_face", "code": "C052", "name": "Goal Roll C052", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "arrow_down", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "P", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "arrow_down", "rotation": 90}, "RIGHT": {"patternId": "P", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "arrow_down", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C052/initial_net.png", "targetTopFaceImage": "../images/C052/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 52, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-052.json"}, "rollSequence": ["S", "E", "W"], "observedPathFaces": [{"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "arrow_down", "rotation": 90}, "RIGHT": {"patternId": "P", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C052\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=arrow_down, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=P, rotation=0]\n [FRONT: patternId=arrow_down, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=P, rotation=0\n- FRONT: patternId=arrow_down, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C052/initial_net.png", "targetTopFaceImage": "images/C052/target_top_face.png"}, "__sample_id__": "C052"} +{"taskType": "roll_to_target_top_face", "code": "C053", "name": "Goal Roll C053", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "9", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "heart", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "9", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "heart", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C053/initial_net.png", "targetTopFaceImage": "../images/C053/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 53, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-053.json"}, "rollSequence": ["S", "S"], "observedPathFaces": [{"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S"]}, "legacy_answer": {"TOP": {"patternId": "9", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C053\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=heart, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=9, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=heart, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=9, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=heart, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C053/initial_net.png", "targetTopFaceImage": "images/C053/target_top_face.png"}, "__sample_id__": "C053"} +{"taskType": "roll_to_target_top_face", "code": "C054", "name": "Goal Roll C054", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "M", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "U", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "5", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "M", "rotation": 0}, "FRONT": {"patternId": "U", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "5", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "U", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C054/initial_net.png", "targetTopFaceImage": "../images/C054/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 54, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-054.json"}, "rollSequence": ["S", "W", "S"], "observedPathFaces": [{"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "M", "rotation": 0}, "FRONT": {"patternId": "U", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "5", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C054\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=U, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=5, rotation=270] [TOP: patternId=M, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=U, rotation=180]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=5, rotation=270\n- TOP: patternId=M, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=U, rotation=180\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C054/initial_net.png", "targetTopFaceImage": "images/C054/target_top_face.png"}, "__sample_id__": "C054"} +{"taskType": "roll_to_target_top_face", "code": "C055", "name": "Goal Roll C055", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "K", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "9", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "9", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "K", "rotation": 180}, "BACK": {"patternId": "9", "rotation": 90}, "LEFT": {"patternId": "9", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "K", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C055/initial_net.png", "targetTopFaceImage": "../images/C055/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 55, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-055.json"}, "rollSequence": ["W", "N", "N"], "observedPathFaces": [{"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "K", "rotation": 180}, "BACK": {"patternId": "9", "rotation": 90}, "LEFT": {"patternId": "9", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C055\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=K, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=9, rotation=90]\n[LEFT: patternId=9, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=K, rotation=180]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=9, rotation=90\n- LEFT: patternId=9, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=K, rotation=180\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C055/initial_net.png", "targetTopFaceImage": "images/C055/target_top_face.png"}, "__sample_id__": "C055"} +{"taskType": "roll_to_target_top_face", "code": "C056", "name": "Goal Roll C056", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "J", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "star", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "J", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "star", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C056/initial_net.png", "targetTopFaceImage": "../images/C056/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 56, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-056.json"}, "rollSequence": ["N", "E"], "observedPathFaces": [{"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "J", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C056\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=star, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=star, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=J, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=star, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=J, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C056/initial_net.png", "targetTopFaceImage": "images/C056/target_top_face.png"}, "__sample_id__": "C056"} +{"taskType": "roll_to_target_top_face", "code": "C057", "name": "Goal Roll C057", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "7", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "J", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "R", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 0}, "RIGHT": {"patternId": "J", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "R", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "7", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C057/initial_net.png", "targetTopFaceImage": "../images/C057/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 57, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-057.json"}, "rollSequence": ["E", "S", "W"], "observedPathFaces": [{"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 0}, "RIGHT": {"patternId": "J", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "R", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C057\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=7, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=J, rotation=270]\n [FRONT: patternId=7, rotation=0]\n [BOTTOM: patternId=R, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=J, rotation=270\n- FRONT: patternId=7, rotation=0\n- BOTTOM: patternId=R, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C057/initial_net.png", "targetTopFaceImage": "images/C057/target_top_face.png"}, "__sample_id__": "C057"} +{"taskType": "roll_to_target_top_face", "code": "C058", "name": "Goal Roll C058", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "J", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "5", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "G", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "J", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "5", "rotation": 90}, "LEFT": {"patternId": "G", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "5", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C058/initial_net.png", "targetTopFaceImage": "../images/C058/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 58, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-058.json"}, "rollSequence": ["N", "W", "N"], "observedPathFaces": [{"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "J", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "5", "rotation": 90}, "LEFT": {"patternId": "G", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C058\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=5, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=5, rotation=90]\n[LEFT: patternId=G, rotation=180] [TOP: patternId=J, rotation=180] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=5, rotation=90\n- LEFT: patternId=G, rotation=180\n- TOP: patternId=J, rotation=180\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C058/initial_net.png", "targetTopFaceImage": "images/C058/target_top_face.png"}, "__sample_id__": "C058"} +{"taskType": "roll_to_target_top_face", "code": "C059", "name": "Goal Roll C059", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "diamond", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "U", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "diamond", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "U", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "U", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C059/initial_net.png", "targetTopFaceImage": "../images/C059/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 59, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-059.json"}, "rollSequence": ["E", "E", "W"], "observedPathFaces": [{"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "W"]}, "legacy_answer": {"TOP": {"patternId": "diamond", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "U", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C059\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=U, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=diamond, rotation=180] [RIGHT: patternId=U, rotation=90]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=diamond, rotation=180\n- RIGHT: patternId=U, rotation=90\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C059/initial_net.png", "targetTopFaceImage": "images/C059/target_top_face.png"}, "__sample_id__": "C059"} +{"taskType": "roll_to_target_top_face", "code": "C060", "name": "Goal Roll C060", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "3", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "M", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "3", "rotation": 90}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "M", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C060/initial_net.png", "targetTopFaceImage": "../images/C060/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 60, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-060.json"}, "rollSequence": ["E", "N"], "observedPathFaces": [{"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "3", "rotation": 90}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C060\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=M, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=M, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=3, rotation=90]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=M, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=3, rotation=90\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C060/initial_net.png", "targetTopFaceImage": "images/C060/target_top_face.png"}, "__sample_id__": "C060"} +{"taskType": "roll_to_target_top_face", "code": "C061", "name": "Goal Roll C061", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "Z", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "D", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "Z", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "D", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "D", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C061/initial_net.png", "targetTopFaceImage": "../images/C061/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 61, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-061.json"}, "rollSequence": ["W", "W"], "observedPathFaces": [{"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W"]}, "legacy_answer": {"TOP": {"patternId": "Z", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "D", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C061\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=D, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=D, rotation=0] [TOP: patternId=Z, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=D, rotation=0\n- TOP: patternId=Z, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C061/initial_net.png", "targetTopFaceImage": "images/C061/target_top_face.png"}, "__sample_id__": "C061"} +{"taskType": "roll_to_target_top_face", "code": "C062", "name": "Goal Roll C062", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "L", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "C", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "L", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "C", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "C", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C062/initial_net.png", "targetTopFaceImage": "../images/C062/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 62, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-062.json"}, "rollSequence": ["E", "E"], "observedPathFaces": [{"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E"]}, "legacy_answer": {"TOP": {"patternId": "L", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "C", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C062\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=C, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=L, rotation=90] [RIGHT: patternId=C, rotation=180]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=L, rotation=90\n- RIGHT: patternId=C, rotation=180\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C062/initial_net.png", "targetTopFaceImage": "images/C062/target_top_face.png"}, "__sample_id__": "C062"} +{"taskType": "roll_to_target_top_face", "code": "C063", "name": "Goal Roll C063", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "H", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "triangle", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "H", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "triangle", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "triangle", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C063/initial_net.png", "targetTopFaceImage": "../images/C063/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 63, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-063.json"}, "rollSequence": ["N", "N"], "observedPathFaces": [{"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N"]}, "legacy_answer": {"TOP": {"patternId": "H", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "triangle", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C063\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=triangle, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=triangle, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=H, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=triangle, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=H, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C063/initial_net.png", "targetTopFaceImage": "images/C063/target_top_face.png"}, "__sample_id__": "C063"} +{"taskType": "roll_to_target_top_face", "code": "C064", "name": "Goal Roll C064", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "O", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "A", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "W", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "O", "rotation": 270}, "FRONT": {"patternId": "A", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "W", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "A", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C064/initial_net.png", "targetTopFaceImage": "../images/C064/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 64, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-064.json"}, "rollSequence": ["S", "W", "S"], "observedPathFaces": [{"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 270}, "FRONT": {"patternId": "A", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "W", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C064\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=A, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=W, rotation=0] [TOP: patternId=O, rotation=270] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=A, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=W, rotation=0\n- TOP: patternId=O, rotation=270\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=A, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C064/initial_net.png", "targetTopFaceImage": "images/C064/target_top_face.png"}, "__sample_id__": "C064"} +{"taskType": "roll_to_target_top_face", "code": "C065", "name": "Goal Roll C065", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "H", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Z", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "H", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Z", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "Z", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C065/initial_net.png", "targetTopFaceImage": "../images/C065/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 65, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-065.json"}, "rollSequence": ["E", "E"], "observedPathFaces": [{"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E"]}, "legacy_answer": {"TOP": {"patternId": "H", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Z", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C065\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=Z, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=H, rotation=90] [RIGHT: patternId=Z, rotation=180]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=H, rotation=90\n- RIGHT: patternId=Z, rotation=180\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C065/initial_net.png", "targetTopFaceImage": "images/C065/target_top_face.png"}, "__sample_id__": "C065"} +{"taskType": "roll_to_target_top_face", "code": "C066", "name": "Goal Roll C066", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "R", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "B", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "V", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "R", "rotation": 270}, "BACK": {"patternId": "B", "rotation": 270}, "LEFT": {"patternId": "V", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "R", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C066/initial_net.png", "targetTopFaceImage": "../images/C066/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 3, "targetRotationOffset": 90, "levelId": 66, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-066.json"}, "rollSequence": ["E", "N", "N"], "observedPathFaces": [{"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "R", "rotation": 270}, "BACK": {"patternId": "B", "rotation": 270}, "LEFT": {"patternId": "V", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C066\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=R, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=B, rotation=270]\n[LEFT: patternId=V, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=R, rotation=270]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=B, rotation=270\n- LEFT: patternId=V, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=R, rotation=270\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C066/initial_net.png", "targetTopFaceImage": "images/C066/target_top_face.png"}, "__sample_id__": "C066"} +{"taskType": "roll_to_target_top_face", "code": "C067", "name": "Goal Roll C067", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "9", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "Y", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "1", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "9", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "Y", "rotation": 90}, "LEFT": {"patternId": "1", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "Y", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C067/initial_net.png", "targetTopFaceImage": "../images/C067/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 67, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-067.json"}, "rollSequence": ["N", "W", "N"], "observedPathFaces": [{"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "9", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "Y", "rotation": 90}, "LEFT": {"patternId": "1", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C067\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=Y, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=Y, rotation=90]\n[LEFT: patternId=1, rotation=90] [TOP: patternId=9, rotation=180] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Y, rotation=90\n- LEFT: patternId=1, rotation=90\n- TOP: patternId=9, rotation=180\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C067/initial_net.png", "targetTopFaceImage": "images/C067/target_top_face.png"}, "__sample_id__": "C067"} +{"taskType": "roll_to_target_top_face", "code": "C068", "name": "Goal Roll C068", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "7", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "diamond", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "7", "rotation": 270}, "FRONT": {"patternId": "diamond", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "diamond", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C068/initial_net.png", "targetTopFaceImage": "../images/C068/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 68, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-068.json"}, "rollSequence": ["S", "S"], "observedPathFaces": [{"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S"]}, "legacy_answer": {"TOP": {"patternId": "7", "rotation": 270}, "FRONT": {"patternId": "diamond", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C068\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=diamond, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=7, rotation=270] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=diamond, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=7, rotation=270\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=diamond, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C068/initial_net.png", "targetTopFaceImage": "images/C068/target_top_face.png"}, "__sample_id__": "C068"} +{"taskType": "roll_to_target_top_face", "code": "C069", "name": "Goal Roll C069", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "H", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "V", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "square", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 270}, "RIGHT": {"patternId": "V", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "square", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "square", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C069/initial_net.png", "targetTopFaceImage": "../images/C069/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 69, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-069.json"}, "rollSequence": ["E", "S", "S"], "observedPathFaces": [{"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 270}, "RIGHT": {"patternId": "V", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "square", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C069\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=square, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=square, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=V, rotation=0]\n [FRONT: patternId=H, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=square, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=V, rotation=0\n- FRONT: patternId=H, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C069/initial_net.png", "targetTopFaceImage": "images/C069/target_top_face.png"}, "__sample_id__": "C069"} +{"taskType": "roll_to_target_top_face", "code": "C070", "name": "Goal Roll C070", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "N", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "heart", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "6", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "N", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "heart", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "6", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "6", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C070/initial_net.png", "targetTopFaceImage": "../images/C070/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 3, "targetRotationOffset": 180, "levelId": 70, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-070.json"}, "rollSequence": ["W", "W", "W"], "observedPathFaces": [{"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "N", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "heart", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "6", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C070\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=6, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=6, rotation=0] [TOP: patternId=N, rotation=0] [RIGHT: patternId=heart, rotation=90]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=6, rotation=0\n- TOP: patternId=N, rotation=0\n- RIGHT: patternId=heart, rotation=90\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C070/initial_net.png", "targetTopFaceImage": "images/C070/target_top_face.png"}, "__sample_id__": "C070"} +{"taskType": "roll_to_target_top_face", "code": "C071", "name": "Goal Roll C071", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "circle", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "H", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "circle", "rotation": 90}, "FRONT": {"patternId": "H", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "H", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C071/initial_net.png", "targetTopFaceImage": "../images/C071/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 71, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-071.json"}, "rollSequence": ["S", "S"], "observedPathFaces": [{"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S"]}, "legacy_answer": {"TOP": {"patternId": "circle", "rotation": 90}, "FRONT": {"patternId": "H", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C071\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=H, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=circle, rotation=90] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=H, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=circle, rotation=90\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=H, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C071/initial_net.png", "targetTopFaceImage": "images/C071/target_top_face.png"}, "__sample_id__": "C071"} +{"taskType": "roll_to_target_top_face", "code": "C072", "name": "Goal Roll C072", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "6", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "D", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_left", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "6", "rotation": 90}, "FRONT": {"patternId": "D", "rotation": 270}, "RIGHT": {"patternId": "arrow_left", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "D", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C072/initial_net.png", "targetTopFaceImage": "../images/C072/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 72, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-072.json"}, "rollSequence": ["E", "S", "E"], "observedPathFaces": [{"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "6", "rotation": 90}, "FRONT": {"patternId": "D", "rotation": 270}, "RIGHT": {"patternId": "arrow_left", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C072\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=D, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=6, rotation=90] [RIGHT: patternId=arrow_left, rotation=180]\n [FRONT: patternId=D, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=6, rotation=90\n- RIGHT: patternId=arrow_left, rotation=180\n- FRONT: patternId=D, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C072/initial_net.png", "targetTopFaceImage": "images/C072/target_top_face.png"}, "__sample_id__": "C072"} +{"taskType": "roll_to_target_top_face", "code": "C073", "name": "Goal Roll C073", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "X", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "5", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "X", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "5", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "X", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C073/initial_net.png", "targetTopFaceImage": "../images/C073/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 73, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-073.json"}, "rollSequence": ["S", "W"], "observedPathFaces": [{"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "X", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "5", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C073\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=X, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=5, rotation=90] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=X, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=5, rotation=90\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=X, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C073/initial_net.png", "targetTopFaceImage": "images/C073/target_top_face.png"}, "__sample_id__": "C073"} +{"taskType": "roll_to_target_top_face", "code": "C074", "name": "Goal Roll C074", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "C", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "S", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "C", "rotation": 0}, "LEFT": {"patternId": "S", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "C", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C074/initial_net.png", "targetTopFaceImage": "../images/C074/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 74, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-074.json"}, "rollSequence": ["W", "N"], "observedPathFaces": [{"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "C", "rotation": 0}, "LEFT": {"patternId": "S", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C074\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=C, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=C, rotation=0]\n[LEFT: patternId=S, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=C, rotation=0\n- LEFT: patternId=S, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C074/initial_net.png", "targetTopFaceImage": "images/C074/target_top_face.png"}, "__sample_id__": "C074"} +{"taskType": "roll_to_target_top_face", "code": "C075", "name": "Goal Roll C075", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "6", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "F", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "6", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "6", "rotation": 0}, "FRONT": {"patternId": "F", "rotation": 180}, "RIGHT": {"patternId": "6", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "F", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C075/initial_net.png", "targetTopFaceImage": "../images/C075/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 75, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-075.json"}, "rollSequence": ["E", "S", "E"], "observedPathFaces": [{"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "6", "rotation": 0}, "FRONT": {"patternId": "F", "rotation": 180}, "RIGHT": {"patternId": "6", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C075\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=F, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=6, rotation=0] [RIGHT: patternId=6, rotation=180]\n [FRONT: patternId=F, rotation=180]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=6, rotation=0\n- RIGHT: patternId=6, rotation=180\n- FRONT: patternId=F, rotation=180\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C075/initial_net.png", "targetTopFaceImage": "images/C075/target_top_face.png"}, "__sample_id__": "C075"} +{"taskType": "roll_to_target_top_face", "code": "C076", "name": "Goal Roll C076", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "star", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "F", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "star", "rotation": 180}, "BACK": {"patternId": "F", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "F", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C076/initial_net.png", "targetTopFaceImage": "../images/C076/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 76, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-076.json"}, "rollSequence": ["E", "N"], "observedPathFaces": [{"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "star", "rotation": 180}, "BACK": {"patternId": "F", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C076\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=F, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=F, rotation=270]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=star, rotation=180]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=F, rotation=270\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=star, rotation=180\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C076/initial_net.png", "targetTopFaceImage": "images/C076/target_top_face.png"}, "__sample_id__": "C076"} +{"taskType": "roll_to_target_top_face", "code": "C077", "name": "Goal Roll C077", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "7", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "J", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "M", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "7", "rotation": 180}, "FRONT": {"patternId": "J", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "J", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C077/initial_net.png", "targetTopFaceImage": "../images/C077/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 3, "targetRotationOffset": 180, "levelId": 77, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-077.json"}, "rollSequence": ["S", "S", "S"], "observedPathFaces": [{"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "7", "rotation": 180}, "FRONT": {"patternId": "J", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C077\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=J, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=M, rotation=90]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=7, rotation=180] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=J, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=M, rotation=90\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=7, rotation=180\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=J, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C077/initial_net.png", "targetTopFaceImage": "images/C077/target_top_face.png"}, "__sample_id__": "C077"} +{"taskType": "roll_to_target_top_face", "code": "C078", "name": "Goal Roll C078", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "M", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "E", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "M", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "E", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "E", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C078/initial_net.png", "targetTopFaceImage": "../images/C078/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 78, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-078.json"}, "rollSequence": ["W", "W"], "observedPathFaces": [{"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W"]}, "legacy_answer": {"TOP": {"patternId": "M", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "E", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C078\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=E, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=E, rotation=270] [TOP: patternId=M, rotation=270] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=E, rotation=270\n- TOP: patternId=M, rotation=270\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C078/initial_net.png", "targetTopFaceImage": "images/C078/target_top_face.png"}, "__sample_id__": "C078"} +{"taskType": "roll_to_target_top_face", "code": "C079", "name": "Goal Roll C079", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "Q", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "star", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "Q", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "star", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "star", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C079/initial_net.png", "targetTopFaceImage": "../images/C079/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 79, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-079.json"}, "rollSequence": ["E", "E"], "observedPathFaces": [{"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E"]}, "legacy_answer": {"TOP": {"patternId": "Q", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "star", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C079\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=star, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=Q, rotation=270] [RIGHT: patternId=star, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=Q, rotation=270\n- RIGHT: patternId=star, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C079/initial_net.png", "targetTopFaceImage": "images/C079/target_top_face.png"}, "__sample_id__": "C079"} +{"taskType": "roll_to_target_top_face", "code": "C080", "name": "Goal Roll C080", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "plus", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "6", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "plus", "rotation": 270}, "RIGHT": {"patternId": "6", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "plus", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C080/initial_net.png", "targetTopFaceImage": "../images/C080/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 80, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-080.json"}, "rollSequence": ["E", "S"], "observedPathFaces": [{"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "plus", "rotation": 270}, "RIGHT": {"patternId": "6", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C080\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=plus, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=6, rotation=180]\n [FRONT: patternId=plus, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=6, rotation=180\n- FRONT: patternId=plus, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C080/initial_net.png", "targetTopFaceImage": "images/C080/target_top_face.png"}, "__sample_id__": "C080"} +{"taskType": "roll_to_target_top_face", "code": "C081", "name": "Goal Roll C081", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "plus", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "C", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "plus", "rotation": 270}, "LEFT": {"patternId": "C", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "plus", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C081/initial_net.png", "targetTopFaceImage": "../images/C081/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 81, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-081.json"}, "rollSequence": ["W", "N", "S"], "observedPathFaces": [{"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "plus", "rotation": 270}, "LEFT": {"patternId": "C", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C081\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=plus, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=plus, rotation=270]\n[LEFT: patternId=C, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=plus, rotation=270\n- LEFT: patternId=C, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C081/initial_net.png", "targetTopFaceImage": "images/C081/target_top_face.png"}, "__sample_id__": "C081"} +{"taskType": "roll_to_target_top_face", "code": "C082", "name": "Goal Roll C082", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "8", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "6", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "8", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "8", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C082/initial_net.png", "targetTopFaceImage": "../images/C082/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 82, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-082.json"}, "rollSequence": ["S", "N"], "observedPathFaces": [{"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "8", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C082\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=8, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=8, rotation=90]\n [BOTTOM: patternId=6, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=8, rotation=90\n- BOTTOM: patternId=6, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C082/initial_net.png", "targetTopFaceImage": "images/C082/target_top_face.png"}, "__sample_id__": "C082"} +{"taskType": "roll_to_target_top_face", "code": "C083", "name": "Goal Roll C083", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "8", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "1", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "8", "rotation": 270}, "RIGHT": {"patternId": "1", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "8", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C083/initial_net.png", "targetTopFaceImage": "../images/C083/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 83, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-083.json"}, "rollSequence": ["S", "E"], "observedPathFaces": [{"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "8", "rotation": 270}, "RIGHT": {"patternId": "1", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C083\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=8, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=1, rotation=90]\n [FRONT: patternId=8, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=1, rotation=90\n- FRONT: patternId=8, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C083/initial_net.png", "targetTopFaceImage": "images/C083/target_top_face.png"}, "__sample_id__": "C083"} +{"taskType": "roll_to_target_top_face", "code": "C084", "name": "Goal Roll C084", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "heart", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "V", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "3", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 180}, "RIGHT": {"patternId": "V", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "V", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C084/initial_net.png", "targetTopFaceImage": "../images/C084/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 3, "targetRotationOffset": 270, "levelId": 84, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-084.json"}, "rollSequence": ["E", "S", "S"], "observedPathFaces": [{"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 180}, "RIGHT": {"patternId": "V", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C084\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=V, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=3, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=V, rotation=0]\n [FRONT: patternId=heart, rotation=180]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=3, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=V, rotation=0\n- FRONT: patternId=heart, rotation=180\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C084/initial_net.png", "targetTopFaceImage": "images/C084/target_top_face.png"}, "__sample_id__": "C084"} +{"taskType": "roll_to_target_top_face", "code": "C085", "name": "Goal Roll C085", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "7", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "square", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "square", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "7", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C085/initial_net.png", "targetTopFaceImage": "../images/C085/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 85, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-085.json"}, "rollSequence": ["S", "W"], "observedPathFaces": [{"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "square", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C085\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=7, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=square, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=7, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=square, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=7, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C085/initial_net.png", "targetTopFaceImage": "images/C085/target_top_face.png"}, "__sample_id__": "C085"} +{"taskType": "roll_to_target_top_face", "code": "C086", "name": "Goal Roll C086", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "K", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "U", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "U", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "K", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C086/initial_net.png", "targetTopFaceImage": "../images/C086/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 86, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-086.json"}, "rollSequence": ["N", "W"], "observedPathFaces": [{"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "U", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C086\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=K, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=K, rotation=270]\n[LEFT: patternId=U, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=K, rotation=270\n- LEFT: patternId=U, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C086/initial_net.png", "targetTopFaceImage": "images/C086/target_top_face.png"}, "__sample_id__": "C086"} +{"taskType": "roll_to_target_top_face", "code": "C087", "name": "Goal Roll C087", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "7", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "circle", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 90}, "RIGHT": {"patternId": "circle", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "7", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C087/initial_net.png", "targetTopFaceImage": "../images/C087/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 87, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-087.json"}, "rollSequence": ["S", "E"], "observedPathFaces": [{"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 90}, "RIGHT": {"patternId": "circle", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C087\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=7, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=circle, rotation=0]\n [FRONT: patternId=7, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=circle, rotation=0\n- FRONT: patternId=7, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C087/initial_net.png", "targetTopFaceImage": "images/C087/target_top_face.png"}, "__sample_id__": "C087"} +{"taskType": "roll_to_target_top_face", "code": "C088", "name": "Goal Roll C088", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "star", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "1", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "plus", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "star", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "1", "rotation": 90}, "BOTTOM": {"patternId": "plus", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "star", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C088/initial_net.png", "targetTopFaceImage": "../images/C088/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 88, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-088.json"}, "rollSequence": ["S", "W", "N"], "observedPathFaces": [{"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "star", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "1", "rotation": 90}, "BOTTOM": {"patternId": "plus", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C088\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=star, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=1, rotation=90] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=star, rotation=270]\n [BOTTOM: patternId=plus, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=1, rotation=90\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=star, rotation=270\n- BOTTOM: patternId=plus, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C088/initial_net.png", "targetTopFaceImage": "images/C088/target_top_face.png"}, "__sample_id__": "C088"} +{"taskType": "roll_to_target_top_face", "code": "C089", "name": "Goal Roll C089", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Y", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "4", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Y", "rotation": 270}, "BACK": {"patternId": "4", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "4", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C089/initial_net.png", "targetTopFaceImage": "../images/C089/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 89, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-089.json"}, "rollSequence": ["N", "E"], "observedPathFaces": [{"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Y", "rotation": 270}, "BACK": {"patternId": "4", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C089\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=4, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=4, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=Y, rotation=270]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=4, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=Y, rotation=270\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C089/initial_net.png", "targetTopFaceImage": "images/C089/target_top_face.png"}, "__sample_id__": "C089"} +{"taskType": "roll_to_target_top_face", "code": "C090", "name": "Goal Roll C090", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "S", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "I", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "circle", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "S", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 270}, "BACK": {"patternId": "circle", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "circle", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C090/initial_net.png", "targetTopFaceImage": "../images/C090/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 90, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-090.json"}, "rollSequence": ["E", "E", "N"], "observedPathFaces": [{"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "S", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 270}, "BACK": {"patternId": "circle", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C090\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=circle, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=circle, rotation=270]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=S, rotation=270] [RIGHT: patternId=I, rotation=270]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=circle, rotation=270\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=S, rotation=270\n- RIGHT: patternId=I, rotation=270\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C090/initial_net.png", "targetTopFaceImage": "images/C090/target_top_face.png"}, "__sample_id__": "C090"} +{"taskType": "roll_to_target_top_face", "code": "C091", "name": "Goal Roll C091", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "smile", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "P", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "smile", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "P", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "P", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C091/initial_net.png", "targetTopFaceImage": "../images/C091/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 91, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-091.json"}, "rollSequence": ["E", "E"], "observedPathFaces": [{"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E"]}, "legacy_answer": {"TOP": {"patternId": "smile", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "P", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C091\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=P, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=smile, rotation=270] [RIGHT: patternId=P, rotation=180]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=smile, rotation=270\n- RIGHT: patternId=P, rotation=180\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C091/initial_net.png", "targetTopFaceImage": "images/C091/target_top_face.png"}, "__sample_id__": "C091"} +{"taskType": "roll_to_target_top_face", "code": "C092", "name": "Goal Roll C092", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "H", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "W", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "W", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "H", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C092/initial_net.png", "targetTopFaceImage": "../images/C092/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 92, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-092.json"}, "rollSequence": ["W", "S"], "observedPathFaces": [{"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "W", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C092\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=H, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=W, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=H, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=W, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=H, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C092/initial_net.png", "targetTopFaceImage": "images/C092/target_top_face.png"}, "__sample_id__": "C092"} +{"taskType": "roll_to_target_top_face", "code": "C093", "name": "Goal Roll C093", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "6", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "heart", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "6", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "heart", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "heart", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C093/initial_net.png", "targetTopFaceImage": "../images/C093/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 93, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-093.json"}, "rollSequence": ["N", "N"], "observedPathFaces": [{"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N"]}, "legacy_answer": {"TOP": {"patternId": "6", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "heart", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C093\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=heart, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=heart, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=6, rotation=90] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=heart, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=6, rotation=90\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C093/initial_net.png", "targetTopFaceImage": "images/C093/target_top_face.png"}, "__sample_id__": "C093"} +{"taskType": "roll_to_target_top_face", "code": "C094", "name": "Goal Roll C094", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "3", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "Z", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 90}, "BOTTOM": {"patternId": "Z", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "3", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C094/initial_net.png", "targetTopFaceImage": "../images/C094/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 94, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-094.json"}, "rollSequence": ["W", "E"], "observedPathFaces": [{"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 90}, "BOTTOM": {"patternId": "Z", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C094\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=3, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=3, rotation=90] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=Z, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=3, rotation=90\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=Z, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C094/initial_net.png", "targetTopFaceImage": "images/C094/target_top_face.png"}, "__sample_id__": "C094"} +{"taskType": "roll_to_target_top_face", "code": "C095", "name": "Goal Roll C095", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_right", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "E", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_right", "rotation": 180}, "LEFT": {"patternId": "E", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "arrow_right", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C095/initial_net.png", "targetTopFaceImage": "../images/C095/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 95, "moveCount": 3, "sourceLevelPath": "levels/reconstruct/generated-095.json"}, "rollSequence": ["N", "W", "E"], "observedPathFaces": [{"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_right", "rotation": 180}, "LEFT": {"patternId": "E", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C095\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=arrow_right, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_right, rotation=180]\n[LEFT: patternId=E, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_right, rotation=180\n- LEFT: patternId=E, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C095/initial_net.png", "targetTopFaceImage": "images/C095/target_top_face.png"}, "__sample_id__": "C095"} +{"taskType": "roll_to_target_top_face", "code": "C096", "name": "Goal Roll C096", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "L", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "V", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "L", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "V", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "V", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C096/initial_net.png", "targetTopFaceImage": "../images/C096/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 96, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-096.json"}, "rollSequence": ["E", "E"], "observedPathFaces": [{"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E"]}, "legacy_answer": {"TOP": {"patternId": "L", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "V", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C096\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=V, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=L, rotation=270] [RIGHT: patternId=V, rotation=270]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=L, rotation=270\n- RIGHT: patternId=V, rotation=270\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C096/initial_net.png", "targetTopFaceImage": "images/C096/target_top_face.png"}, "__sample_id__": "C096"} +{"taskType": "roll_to_target_top_face", "code": "C097", "name": "Goal Roll C097", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "3", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "I", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "3", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "I", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "I", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C097/initial_net.png", "targetTopFaceImage": "../images/C097/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 97, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-097.json"}, "rollSequence": ["W", "W"], "observedPathFaces": [{"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W"]}, "legacy_answer": {"TOP": {"patternId": "3", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "I", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C097\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=I, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=I, rotation=180] [TOP: patternId=3, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=I, rotation=180\n- TOP: patternId=3, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C097/initial_net.png", "targetTopFaceImage": "images/C097/target_top_face.png"}, "__sample_id__": "C097"} +{"taskType": "roll_to_target_top_face", "code": "C098", "name": "Goal Roll C098", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "circle", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "S", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "circle", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "S", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C098/initial_net.png", "targetTopFaceImage": "../images/C098/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 98, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-098.json"}, "rollSequence": ["E", "E"], "observedPathFaces": [{"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E"]}, "legacy_answer": {"TOP": {"patternId": "circle", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C098\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=S, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=circle, rotation=90] [RIGHT: patternId=S, rotation=180]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=circle, rotation=90\n- RIGHT: patternId=S, rotation=180\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C098/initial_net.png", "targetTopFaceImage": "images/C098/target_top_face.png"}, "__sample_id__": "C098"} +{"taskType": "roll_to_target_top_face", "code": "C099", "name": "Goal Roll C099", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "6", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "G", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "6", "rotation": 90}, "FRONT": {"patternId": "G", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "G", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C099/initial_net.png", "targetTopFaceImage": "../images/C099/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 99, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-099.json"}, "rollSequence": ["S", "S"], "observedPathFaces": [{"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S"]}, "legacy_answer": {"TOP": {"patternId": "6", "rotation": 90}, "FRONT": {"patternId": "G", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C099\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=G, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=6, rotation=90] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=G, rotation=180]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=6, rotation=90\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=G, rotation=180\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C099/initial_net.png", "targetTopFaceImage": "images/C099/target_top_face.png"}, "__sample_id__": "C099"} +{"taskType": "roll_to_target_top_face", "code": "C100", "name": "Goal Roll C100", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_right", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "star", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 180}, "BACK": {"patternId": "star", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "star", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C100/initial_net.png", "targetTopFaceImage": "../images/C100/target_top_face.png"}, "metadata": {"difficulty": 1, "tier": 1, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 100, "moveCount": 2, "sourceLevelPath": "levels/reconstruct/generated-100.json"}, "rollSequence": ["N", "E"], "observedPathFaces": [{"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 180}, "BACK": {"patternId": "star", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C100\n- task_type: roll_to_target_top_face\n- difficulty: 1\n- target_top_face: patternId=star, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=star, rotation=270]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=arrow_right, rotation=180]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=star, rotation=270\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=arrow_right, rotation=180\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C100/initial_net.png", "targetTopFaceImage": "images/C100/target_top_face.png"}, "__sample_id__": "C100"} +{"taskType": "roll_to_target_top_face", "code": "C101", "name": "Goal Roll C101", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "W", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "circle", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "U", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "Z", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "W", "rotation": 90}, "BACK": {"patternId": "circle", "rotation": 270}, "LEFT": {"patternId": "U", "rotation": 90}, "BOTTOM": {"patternId": "Z", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "W", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C101/initial_net.png", "targetTopFaceImage": "../images/C101/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 101, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-101.json"}, "rollSequence": ["W", "N", "E", "N"], "observedPathFaces": [{"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "W", "rotation": 90}, "BACK": {"patternId": "circle", "rotation": 270}, "LEFT": {"patternId": "U", "rotation": 90}, "BOTTOM": {"patternId": "Z", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C101\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=W, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=circle, rotation=270]\n[LEFT: patternId=U, rotation=90] [TOP: patternId=?, rotation=0] [RIGHT: patternId=W, rotation=90]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=Z, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=circle, rotation=270\n- LEFT: patternId=U, rotation=90\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=W, rotation=90\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=Z, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C101/initial_net.png", "targetTopFaceImage": "images/C101/target_top_face.png"}, "__sample_id__": "C101"} +{"taskType": "roll_to_target_top_face", "code": "C102", "name": "Goal Roll C102", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_right", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "7", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "5", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 180}, "BACK": {"patternId": "7", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "5", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "7", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C102/initial_net.png", "targetTopFaceImage": "../images/C102/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 102, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-102.json"}, "rollSequence": ["N", "E", "W", "S", "N"], "observedPathFaces": [{"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "W", "S", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 180}, "BACK": {"patternId": "7", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "5", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C102\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=7, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=7, rotation=270]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=arrow_right, rotation=180]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=5, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=7, rotation=270\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=arrow_right, rotation=180\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=5, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C102/initial_net.png", "targetTopFaceImage": "images/C102/target_top_face.png"}, "__sample_id__": "C102"} +{"taskType": "roll_to_target_top_face", "code": "C103", "name": "Goal Roll C103", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "R", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "R", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "X", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "V", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "R", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "R", "rotation": 270}, "BACK": {"patternId": "X", "rotation": 180}, "LEFT": {"patternId": "V", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "R", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C103/initial_net.png", "targetTopFaceImage": "../images/C103/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 5, "targetRotationOffset": 90, "levelId": 103, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-103.json"}, "rollSequence": ["N", "E", "W", "N", "W"], "observedPathFaces": [{"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "W", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "R", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "R", "rotation": 270}, "BACK": {"patternId": "X", "rotation": 180}, "LEFT": {"patternId": "V", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C103\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=R, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=X, rotation=180]\n[LEFT: patternId=V, rotation=90] [TOP: patternId=R, rotation=180] [RIGHT: patternId=R, rotation=270]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=X, rotation=180\n- LEFT: patternId=V, rotation=90\n- TOP: patternId=R, rotation=180\n- RIGHT: patternId=R, rotation=270\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C103/initial_net.png", "targetTopFaceImage": "images/C103/target_top_face.png"}, "__sample_id__": "C103"} +{"taskType": "roll_to_target_top_face", "code": "C104", "name": "Goal Roll C104", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "M", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "R", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "S", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "M", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "R", "rotation": 90}, "LEFT": {"patternId": "S", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "R", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C104/initial_net.png", "targetTopFaceImage": "../images/C104/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 104, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-104.json"}, "rollSequence": ["N", "W", "N", "E"], "observedPathFaces": [{"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "M", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "R", "rotation": 90}, "LEFT": {"patternId": "S", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C104\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=R, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=R, rotation=90]\n[LEFT: patternId=S, rotation=180] [TOP: patternId=M, rotation=270] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=R, rotation=90\n- LEFT: patternId=S, rotation=180\n- TOP: patternId=M, rotation=270\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C104/initial_net.png", "targetTopFaceImage": "images/C104/target_top_face.png"}, "__sample_id__": "C104"} +{"taskType": "roll_to_target_top_face", "code": "C105", "name": "Goal Roll C105", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "V", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "L", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "8", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "V", "rotation": 270}, "FRONT": {"patternId": "L", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "L", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C105/initial_net.png", "targetTopFaceImage": "../images/C105/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 105, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-105.json"}, "rollSequence": ["W", "S", "W", "E"], "observedPathFaces": [{"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "W", "E"]}, "legacy_answer": {"TOP": {"patternId": "V", "rotation": 270}, "FRONT": {"patternId": "L", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C105\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=L, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=8, rotation=90] [TOP: patternId=V, rotation=270] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=L, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=8, rotation=90\n- TOP: patternId=V, rotation=270\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=L, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C105/initial_net.png", "targetTopFaceImage": "images/C105/target_top_face.png"}, "__sample_id__": "C105"} +{"taskType": "roll_to_target_top_face", "code": "C106", "name": "Goal Roll C106", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "M", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "L", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "star", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "diamond", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "U", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "M", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "L", "rotation": 180}, "BACK": {"patternId": "star", "rotation": 90}, "LEFT": {"patternId": "diamond", "rotation": 270}, "BOTTOM": {"patternId": "U", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "L", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C106/initial_net.png", "targetTopFaceImage": "../images/C106/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 4, "targetRotationOffset": 270, "levelId": 106, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-106.json"}, "rollSequence": ["E", "N", "W", "N", "N"], "observedPathFaces": [{"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "W", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "M", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "L", "rotation": 180}, "BACK": {"patternId": "star", "rotation": 90}, "LEFT": {"patternId": "diamond", "rotation": 270}, "BOTTOM": {"patternId": "U", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C106\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=L, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=star, rotation=90]\n[LEFT: patternId=diamond, rotation=270] [TOP: patternId=M, rotation=90] [RIGHT: patternId=L, rotation=180]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=U, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=star, rotation=90\n- LEFT: patternId=diamond, rotation=270\n- TOP: patternId=M, rotation=90\n- RIGHT: patternId=L, rotation=180\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=U, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C106/initial_net.png", "targetTopFaceImage": "images/C106/target_top_face.png"}, "__sample_id__": "C106"} +{"taskType": "roll_to_target_top_face", "code": "C107", "name": "Goal Roll C107", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "H", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "6", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "Z", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "X", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "8", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 180}, "RIGHT": {"patternId": "6", "rotation": 270}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "X", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "Z", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C107/initial_net.png", "targetTopFaceImage": "../images/C107/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 5, "targetRotationOffset": 90, "levelId": 107, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-107.json"}, "rollSequence": ["W", "N", "E", "N", "E"], "observedPathFaces": [{"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "E", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 180}, "RIGHT": {"patternId": "6", "rotation": 270}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "X", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C107\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=Z, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=Z, rotation=90]\n[LEFT: patternId=X, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=6, rotation=270]\n [FRONT: patternId=H, rotation=180]\n [BOTTOM: patternId=8, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Z, rotation=90\n- LEFT: patternId=X, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=6, rotation=270\n- FRONT: patternId=H, rotation=180\n- BOTTOM: patternId=8, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C107/initial_net.png", "targetTopFaceImage": "images/C107/target_top_face.png"}, "__sample_id__": "C107"} +{"taskType": "roll_to_target_top_face", "code": "C108", "name": "Goal Roll C108", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "square", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "smile", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_left", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "B", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "square", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "smile", "rotation": 270}, "BACK": {"patternId": "arrow_left", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "B", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "B", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C108/initial_net.png", "targetTopFaceImage": "../images/C108/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 4, "targetRotationOffset": 180, "levelId": 108, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-108.json"}, "rollSequence": ["E", "W", "N", "N"], "observedPathFaces": [{"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "W", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "square", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "smile", "rotation": 270}, "BACK": {"patternId": "arrow_left", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "B", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C108\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=B, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_left, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=square, rotation=270] [RIGHT: patternId=smile, rotation=270]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=B, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_left, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=square, rotation=270\n- RIGHT: patternId=smile, rotation=270\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=B, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C108/initial_net.png", "targetTopFaceImage": "images/C108/target_top_face.png"}, "__sample_id__": "C108"} +{"taskType": "roll_to_target_top_face", "code": "C109", "name": "Goal Roll C109", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "9", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "B", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "1", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "5", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "9", "rotation": 0}, "FRONT": {"patternId": "B", "rotation": 180}, "RIGHT": {"patternId": "1", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "5", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "5", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C109/initial_net.png", "targetTopFaceImage": "../images/C109/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 2, "targetRotationOffset": 180, "levelId": 109, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-109.json"}, "rollSequence": ["E", "E", "S", "S"], "observedPathFaces": [{"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "9", "rotation": 0}, "FRONT": {"patternId": "B", "rotation": 180}, "RIGHT": {"patternId": "1", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "5", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C109\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=5, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=9, rotation=0] [RIGHT: patternId=1, rotation=270]\n [FRONT: patternId=B, rotation=180]\n [BOTTOM: patternId=5, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=9, rotation=0\n- RIGHT: patternId=1, rotation=270\n- FRONT: patternId=B, rotation=180\n- BOTTOM: patternId=5, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C109/initial_net.png", "targetTopFaceImage": "images/C109/target_top_face.png"}, "__sample_id__": "C109"} +{"taskType": "roll_to_target_top_face", "code": "C110", "name": "Goal Roll C110", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "arrow_right", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "T", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "J", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "arrow_right", "rotation": 0}, "RIGHT": {"patternId": "T", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "J", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "arrow_right", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C110/initial_net.png", "targetTopFaceImage": "../images/C110/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 110, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-110.json"}, "rollSequence": ["E", "S", "W", "E"], "observedPathFaces": [{"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "W", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "arrow_right", "rotation": 0}, "RIGHT": {"patternId": "T", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "J", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C110\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=arrow_right, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=T, rotation=270]\n [FRONT: patternId=arrow_right, rotation=0]\n [BOTTOM: patternId=J, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=T, rotation=270\n- FRONT: patternId=arrow_right, rotation=0\n- BOTTOM: patternId=J, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C110/initial_net.png", "targetTopFaceImage": "images/C110/target_top_face.png"}, "__sample_id__": "C110"} +{"taskType": "roll_to_target_top_face", "code": "C111", "name": "Goal Roll C111", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "Y", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "diamond", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "H", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "Y", "rotation": 0}, "RIGHT": {"patternId": "diamond", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "H", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "Y", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C111/initial_net.png", "targetTopFaceImage": "../images/C111/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 111, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-111.json"}, "rollSequence": ["E", "S", "W", "N"], "observedPathFaces": [{"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "Y", "rotation": 0}, "RIGHT": {"patternId": "diamond", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "H", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C111\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=Y, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=diamond, rotation=0]\n [FRONT: patternId=Y, rotation=0]\n [BOTTOM: patternId=H, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=diamond, rotation=0\n- FRONT: patternId=Y, rotation=0\n- BOTTOM: patternId=H, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C111/initial_net.png", "targetTopFaceImage": "images/C111/target_top_face.png"}, "__sample_id__": "C111"} +{"taskType": "roll_to_target_top_face", "code": "C112", "name": "Goal Roll C112", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "L", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_down", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_down", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "L", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_down", "rotation": 270}, "BOTTOM": {"patternId": "arrow_down", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "L", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C112/initial_net.png", "targetTopFaceImage": "../images/C112/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 112, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-112.json"}, "rollSequence": ["W", "S", "E", "N"], "observedPathFaces": [{"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "L", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_down", "rotation": 270}, "BOTTOM": {"patternId": "arrow_down", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C112\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=L, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=arrow_down, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=L, rotation=90]\n [BOTTOM: patternId=arrow_down, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=arrow_down, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=L, rotation=90\n- BOTTOM: patternId=arrow_down, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C112/initial_net.png", "targetTopFaceImage": "images/C112/target_top_face.png"}, "__sample_id__": "C112"} +{"taskType": "roll_to_target_top_face", "code": "C113", "name": "Goal Roll C113", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Q", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_down", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "circle", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "W", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Q", "rotation": 0}, "BACK": {"patternId": "arrow_down", "rotation": 270}, "LEFT": {"patternId": "circle", "rotation": 90}, "BOTTOM": {"patternId": "W", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "circle", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C113/initial_net.png", "targetTopFaceImage": "../images/C113/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 3, "targetRotationOffset": 270, "levelId": 113, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-113.json"}, "rollSequence": ["W", "N", "N", "E", "S"], "observedPathFaces": [{"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "N", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Q", "rotation": 0}, "BACK": {"patternId": "arrow_down", "rotation": 270}, "LEFT": {"patternId": "circle", "rotation": 90}, "BOTTOM": {"patternId": "W", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C113\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=circle, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_down, rotation=270]\n[LEFT: patternId=circle, rotation=90] [TOP: patternId=?, rotation=0] [RIGHT: patternId=Q, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=W, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_down, rotation=270\n- LEFT: patternId=circle, rotation=90\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=Q, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=W, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C113/initial_net.png", "targetTopFaceImage": "images/C113/target_top_face.png"}, "__sample_id__": "C113"} +{"taskType": "roll_to_target_top_face", "code": "C114", "name": "Goal Roll C114", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "W", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "Q", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "T", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "C", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "W", "rotation": 0}, "FRONT": {"patternId": "Q", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "T", "rotation": 0}, "BOTTOM": {"patternId": "C", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "W", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C114/initial_net.png", "targetTopFaceImage": "../images/C114/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 3, "targetRotationOffset": 270, "levelId": 114, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-114.json"}, "rollSequence": ["W", "S", "E", "N", "N"], "observedPathFaces": [{"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "E", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "W", "rotation": 0}, "FRONT": {"patternId": "Q", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "T", "rotation": 0}, "BOTTOM": {"patternId": "C", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C114\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=W, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=T, rotation=0] [TOP: patternId=W, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=Q, rotation=0]\n [BOTTOM: patternId=C, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=T, rotation=0\n- TOP: patternId=W, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=Q, rotation=0\n- BOTTOM: patternId=C, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C114/initial_net.png", "targetTopFaceImage": "images/C114/target_top_face.png"}, "__sample_id__": "C114"} +{"taskType": "roll_to_target_top_face", "code": "C115", "name": "Goal Roll C115", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "circle", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "plus", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "circle", "rotation": 90}, "RIGHT": {"patternId": "plus", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "circle", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C115/initial_net.png", "targetTopFaceImage": "../images/C115/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 115, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-115.json"}, "rollSequence": ["E", "S", "N", "S"], "observedPathFaces": [{"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "N", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "circle", "rotation": 90}, "RIGHT": {"patternId": "plus", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C115\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=circle, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=plus, rotation=0]\n [FRONT: patternId=circle, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=plus, rotation=0\n- FRONT: patternId=circle, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C115/initial_net.png", "targetTopFaceImage": "images/C115/target_top_face.png"}, "__sample_id__": "C115"} +{"taskType": "roll_to_target_top_face", "code": "C116", "name": "Goal Roll C116", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "S", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Z", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "L", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "2", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "S", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Z", "rotation": 90}, "BACK": {"patternId": "L", "rotation": 0}, "LEFT": {"patternId": "2", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "Z", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C116/initial_net.png", "targetTopFaceImage": "../images/C116/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 4, "targetRotationOffset": 180, "levelId": 116, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-116.json"}, "rollSequence": ["E", "N", "E", "N", "W"], "observedPathFaces": [{"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "E", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "S", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Z", "rotation": 90}, "BACK": {"patternId": "L", "rotation": 0}, "LEFT": {"patternId": "2", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C116\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=Z, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=L, rotation=0]\n[LEFT: patternId=2, rotation=180] [TOP: patternId=S, rotation=90] [RIGHT: patternId=Z, rotation=90]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=L, rotation=0\n- LEFT: patternId=2, rotation=180\n- TOP: patternId=S, rotation=90\n- RIGHT: patternId=Z, rotation=90\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C116/initial_net.png", "targetTopFaceImage": "images/C116/target_top_face.png"}, "__sample_id__": "C116"} +{"taskType": "roll_to_target_top_face", "code": "C117", "name": "Goal Roll C117", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "8", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "O", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Z", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "L", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "1", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "8", "rotation": 90}, "FRONT": {"patternId": "O", "rotation": 0}, "RIGHT": {"patternId": "Z", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "L", "rotation": 90}, "BOTTOM": {"patternId": "1", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "1", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C117/initial_net.png", "targetTopFaceImage": "../images/C117/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 5, "targetRotationOffset": 90, "levelId": 117, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-117.json"}, "rollSequence": ["S", "E", "N", "N", "N"], "observedPathFaces": [{"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "N", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "8", "rotation": 90}, "FRONT": {"patternId": "O", "rotation": 0}, "RIGHT": {"patternId": "Z", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "L", "rotation": 90}, "BOTTOM": {"patternId": "1", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C117\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=1, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=L, rotation=90] [TOP: patternId=8, rotation=90] [RIGHT: patternId=Z, rotation=0]\n [FRONT: patternId=O, rotation=0]\n [BOTTOM: patternId=1, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=L, rotation=90\n- TOP: patternId=8, rotation=90\n- RIGHT: patternId=Z, rotation=0\n- FRONT: patternId=O, rotation=0\n- BOTTOM: patternId=1, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C117/initial_net.png", "targetTopFaceImage": "images/C117/target_top_face.png"}, "__sample_id__": "C117"} +{"taskType": "roll_to_target_top_face", "code": "C118", "name": "Goal Roll C118", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "F", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "W", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "4", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "D", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "F", "rotation": 180}, "FRONT": {"patternId": "W", "rotation": 270}, "RIGHT": {"patternId": "4", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "D", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "D", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C118/initial_net.png", "targetTopFaceImage": "../images/C118/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 5, "targetRotationOffset": 90, "levelId": 118, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-118.json"}, "rollSequence": ["E", "S", "W", "N", "N"], "observedPathFaces": [{"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "W", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "F", "rotation": 180}, "FRONT": {"patternId": "W", "rotation": 270}, "RIGHT": {"patternId": "4", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "D", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C118\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=D, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=F, rotation=180] [RIGHT: patternId=4, rotation=90]\n [FRONT: patternId=W, rotation=270]\n [BOTTOM: patternId=D, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=F, rotation=180\n- RIGHT: patternId=4, rotation=90\n- FRONT: patternId=W, rotation=270\n- BOTTOM: patternId=D, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C118/initial_net.png", "targetTopFaceImage": "images/C118/target_top_face.png"}, "__sample_id__": "C118"} +{"taskType": "roll_to_target_top_face", "code": "C119", "name": "Goal Roll C119", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "8", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "G", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "N", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "W", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "8", "rotation": 180}, "FRONT": {"patternId": "G", "rotation": 270}, "RIGHT": {"patternId": "N", "rotation": 90}, "BACK": {"patternId": "W", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "W", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C119/initial_net.png", "targetTopFaceImage": "../images/C119/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 2, "targetRotationOffset": 180, "levelId": 119, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-119.json"}, "rollSequence": ["E", "S", "E", "E"], "observedPathFaces": [{"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "8", "rotation": 180}, "FRONT": {"patternId": "G", "rotation": 270}, "RIGHT": {"patternId": "N", "rotation": 90}, "BACK": {"patternId": "W", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C119\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=W, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=W, rotation=270]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=8, rotation=180] [RIGHT: patternId=N, rotation=90]\n [FRONT: patternId=G, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=W, rotation=270\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=8, rotation=180\n- RIGHT: patternId=N, rotation=90\n- FRONT: patternId=G, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C119/initial_net.png", "targetTopFaceImage": "images/C119/target_top_face.png"}, "__sample_id__": "C119"} +{"taskType": "roll_to_target_top_face", "code": "C120", "name": "Goal Roll C120", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "plus", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "V", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "O", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "plus", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "V", "rotation": 270}, "LEFT": {"patternId": "O", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "V", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C120/initial_net.png", "targetTopFaceImage": "../images/C120/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 120, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-120.json"}, "rollSequence": ["N", "N", "W", "E", "S"], "observedPathFaces": [{"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "W", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "plus", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "V", "rotation": 270}, "LEFT": {"patternId": "O", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C120\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=V, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=V, rotation=270]\n[LEFT: patternId=O, rotation=90] [TOP: patternId=plus, rotation=90] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=V, rotation=270\n- LEFT: patternId=O, rotation=90\n- TOP: patternId=plus, rotation=90\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C120/initial_net.png", "targetTopFaceImage": "images/C120/target_top_face.png"}, "__sample_id__": "C120"} +{"taskType": "roll_to_target_top_face", "code": "C121", "name": "Goal Roll C121", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "A", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "diamond", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "S", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "G", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "V", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "A", "rotation": 90}, "FRONT": {"patternId": "diamond", "rotation": 180}, "RIGHT": {"patternId": "S", "rotation": 0}, "BACK": {"patternId": "G", "rotation": 180}, "LEFT": {"patternId": "V", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "S", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C121/initial_net.png", "targetTopFaceImage": "../images/C121/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 4, "targetRotationOffset": 270, "levelId": 121, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-121.json"}, "rollSequence": ["E", "E", "N", "E", "E"], "observedPathFaces": [{"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "N", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "A", "rotation": 90}, "FRONT": {"patternId": "diamond", "rotation": 180}, "RIGHT": {"patternId": "S", "rotation": 0}, "BACK": {"patternId": "G", "rotation": 180}, "LEFT": {"patternId": "V", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C121\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=S, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=G, rotation=180]\n[LEFT: patternId=V, rotation=90] [TOP: patternId=A, rotation=90] [RIGHT: patternId=S, rotation=0]\n [FRONT: patternId=diamond, rotation=180]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=G, rotation=180\n- LEFT: patternId=V, rotation=90\n- TOP: patternId=A, rotation=90\n- RIGHT: patternId=S, rotation=0\n- FRONT: patternId=diamond, rotation=180\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C121/initial_net.png", "targetTopFaceImage": "images/C121/target_top_face.png"}, "__sample_id__": "C121"} +{"taskType": "roll_to_target_top_face", "code": "C122", "name": "Goal Roll C122", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "T", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "8", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "1", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "A", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "T", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "8", "rotation": 90}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "A", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "8", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C122/initial_net.png", "targetTopFaceImage": "../images/C122/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 3, "targetRotationOffset": 270, "levelId": 122, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-122.json"}, "rollSequence": ["E", "E", "E", "N", "W"], "observedPathFaces": [{"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "E", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "T", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "8", "rotation": 90}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "A", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C122\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=8, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=1, rotation=180]\n[LEFT: patternId=A, rotation=180] [TOP: patternId=T, rotation=0] [RIGHT: patternId=8, rotation=90]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=1, rotation=180\n- LEFT: patternId=A, rotation=180\n- TOP: patternId=T, rotation=0\n- RIGHT: patternId=8, rotation=90\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C122/initial_net.png", "targetTopFaceImage": "images/C122/target_top_face.png"}, "__sample_id__": "C122"} +{"taskType": "roll_to_target_top_face", "code": "C123", "name": "Goal Roll C123", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "S", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_up", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "diamond", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "2", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 270}, "BACK": {"patternId": "arrow_up", "rotation": 90}, "LEFT": {"patternId": "diamond", "rotation": 180}, "BOTTOM": {"patternId": "2", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "S", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C123/initial_net.png", "targetTopFaceImage": "../images/C123/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 4, "targetRotationOffset": 180, "levelId": 123, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-123.json"}, "rollSequence": ["N", "E", "S", "S"], "observedPathFaces": [{"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 270}, "BACK": {"patternId": "arrow_up", "rotation": 90}, "LEFT": {"patternId": "diamond", "rotation": 180}, "BOTTOM": {"patternId": "2", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C123\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=S, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_up, rotation=90]\n[LEFT: patternId=diamond, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=S, rotation=270]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=2, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_up, rotation=90\n- LEFT: patternId=diamond, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=S, rotation=270\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=2, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C123/initial_net.png", "targetTopFaceImage": "images/C123/target_top_face.png"}, "__sample_id__": "C123"} +{"taskType": "roll_to_target_top_face", "code": "C124", "name": "Goal Roll C124", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "P", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "O", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "circle", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_left", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_left", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "P", "rotation": 90}, "RIGHT": {"patternId": "O", "rotation": 270}, "BACK": {"patternId": "circle", "rotation": 180}, "LEFT": {"patternId": "arrow_left", "rotation": 0}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "circle", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C124/initial_net.png", "targetTopFaceImage": "../images/C124/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 124, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-124.json"}, "rollSequence": ["S", "W", "W", "W", "N"], "observedPathFaces": [{"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "W", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "P", "rotation": 90}, "RIGHT": {"patternId": "O", "rotation": 270}, "BACK": {"patternId": "circle", "rotation": 180}, "LEFT": {"patternId": "arrow_left", "rotation": 0}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C124\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=circle, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=circle, rotation=180]\n[LEFT: patternId=arrow_left, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=O, rotation=270]\n [FRONT: patternId=P, rotation=90]\n [BOTTOM: patternId=arrow_left, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=circle, rotation=180\n- LEFT: patternId=arrow_left, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=O, rotation=270\n- FRONT: patternId=P, rotation=90\n- BOTTOM: patternId=arrow_left, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C124/initial_net.png", "targetTopFaceImage": "images/C124/target_top_face.png"}, "__sample_id__": "C124"} +{"taskType": "roll_to_target_top_face", "code": "C125", "name": "Goal Roll C125", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "square", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "K", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "circle", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "O", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "square", "rotation": 90}, "FRONT": {"patternId": "K", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 90}, "LEFT": {"patternId": "O", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "circle", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C125/initial_net.png", "targetTopFaceImage": "../images/C125/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 2, "targetRotationOffset": 270, "levelId": 125, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-125.json"}, "rollSequence": ["W", "S", "W", "W", "E"], "observedPathFaces": [{"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "W", "W", "E"]}, "legacy_answer": {"TOP": {"patternId": "square", "rotation": 90}, "FRONT": {"patternId": "K", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 90}, "LEFT": {"patternId": "O", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C125\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=circle, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=circle, rotation=90]\n[LEFT: patternId=O, rotation=90] [TOP: patternId=square, rotation=90] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=K, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=circle, rotation=90\n- LEFT: patternId=O, rotation=90\n- TOP: patternId=square, rotation=90\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=K, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C125/initial_net.png", "targetTopFaceImage": "images/C125/target_top_face.png"}, "__sample_id__": "C125"} +{"taskType": "roll_to_target_top_face", "code": "C126", "name": "Goal Roll C126", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "D", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "R", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "diamond", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "2", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 180}, "RIGHT": {"patternId": "R", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "diamond", "rotation": 270}, "BOTTOM": {"patternId": "2", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "R", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C126/initial_net.png", "targetTopFaceImage": "../images/C126/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 5, "targetRotationOffset": 90, "levelId": 126, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-126.json"}, "rollSequence": ["W", "S", "S", "E", "E"], "observedPathFaces": [{"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "S", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 180}, "RIGHT": {"patternId": "R", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "diamond", "rotation": 270}, "BOTTOM": {"patternId": "2", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C126\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=R, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=diamond, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=R, rotation=180]\n [FRONT: patternId=D, rotation=180]\n [BOTTOM: patternId=2, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=diamond, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=R, rotation=180\n- FRONT: patternId=D, rotation=180\n- BOTTOM: patternId=2, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C126/initial_net.png", "targetTopFaceImage": "images/C126/target_top_face.png"}, "__sample_id__": "C126"} +{"taskType": "roll_to_target_top_face", "code": "C127", "name": "Goal Roll C127", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "9", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "7", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "X", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "9", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "7", "rotation": 180}, "LEFT": {"patternId": "X", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "7", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C127/initial_net.png", "targetTopFaceImage": "../images/C127/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 127, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-127.json"}, "rollSequence": ["N", "N", "S", "W"], "observedPathFaces": [{"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "9", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "7", "rotation": 180}, "LEFT": {"patternId": "X", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C127\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=7, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=7, rotation=180]\n[LEFT: patternId=X, rotation=0] [TOP: patternId=9, rotation=270] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=7, rotation=180\n- LEFT: patternId=X, rotation=0\n- TOP: patternId=9, rotation=270\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C127/initial_net.png", "targetTopFaceImage": "images/C127/target_top_face.png"}, "__sample_id__": "C127"} +{"taskType": "roll_to_target_top_face", "code": "C128", "name": "Goal Roll C128", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "square", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "circle", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "N", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "circle", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "square", "rotation": 180}, "FRONT": {"patternId": "circle", "rotation": 270}, "RIGHT": {"patternId": "N", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "circle", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C128/initial_net.png", "targetTopFaceImage": "../images/C128/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 128, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-128.json"}, "rollSequence": ["E", "S", "E", "S"], "observedPathFaces": [{"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "square", "rotation": 180}, "FRONT": {"patternId": "circle", "rotation": 270}, "RIGHT": {"patternId": "N", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C128\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=circle, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=circle, rotation=270] [TOP: patternId=square, rotation=180] [RIGHT: patternId=N, rotation=0]\n [FRONT: patternId=circle, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=circle, rotation=270\n- TOP: patternId=square, rotation=180\n- RIGHT: patternId=N, rotation=0\n- FRONT: patternId=circle, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C128/initial_net.png", "targetTopFaceImage": "images/C128/target_top_face.png"}, "__sample_id__": "C128"} +{"taskType": "roll_to_target_top_face", "code": "C129", "name": "Goal Roll C129", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "X", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "D", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "F", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "X", "rotation": 180}, "RIGHT": {"patternId": "D", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "F", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "X", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C129/initial_net.png", "targetTopFaceImage": "../images/C129/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 129, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-129.json"}, "rollSequence": ["E", "S", "W", "N"], "observedPathFaces": [{"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "X", "rotation": 180}, "RIGHT": {"patternId": "D", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "F", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C129\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=X, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=D, rotation=90]\n [FRONT: patternId=X, rotation=180]\n [BOTTOM: patternId=F, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=D, rotation=90\n- FRONT: patternId=X, rotation=180\n- BOTTOM: patternId=F, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C129/initial_net.png", "targetTopFaceImage": "images/C129/target_top_face.png"}, "__sample_id__": "C129"} +{"taskType": "roll_to_target_top_face", "code": "C130", "name": "Goal Roll C130", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "M", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "V", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "Z", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "plus", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "M", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "V", "rotation": 90}, "LEFT": {"patternId": "Z", "rotation": 270}, "BOTTOM": {"patternId": "plus", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "plus", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C130/initial_net.png", "targetTopFaceImage": "../images/C130/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 2, "targetRotationOffset": 180, "levelId": 130, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-130.json"}, "rollSequence": ["N", "N", "W", "S", "W"], "observedPathFaces": [{"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "W", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "M", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "V", "rotation": 90}, "LEFT": {"patternId": "Z", "rotation": 270}, "BOTTOM": {"patternId": "plus", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C130\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=plus, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=V, rotation=90]\n[LEFT: patternId=Z, rotation=270] [TOP: patternId=M, rotation=180] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=plus, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=V, rotation=90\n- LEFT: patternId=Z, rotation=270\n- TOP: patternId=M, rotation=180\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=plus, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C130/initial_net.png", "targetTopFaceImage": "images/C130/target_top_face.png"}, "__sample_id__": "C130"} +{"taskType": "roll_to_target_top_face", "code": "C131", "name": "Goal Roll C131", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "arrow_left", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "E", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "J", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "I", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "arrow_left", "rotation": 90}, "FRONT": {"patternId": "E", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "J", "rotation": 180}, "BOTTOM": {"patternId": "I", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "I", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C131/initial_net.png", "targetTopFaceImage": "../images/C131/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 2, "targetRotationOffset": 270, "levelId": 131, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-131.json"}, "rollSequence": ["W", "W", "S", "S"], "observedPathFaces": [{"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "arrow_left", "rotation": 90}, "FRONT": {"patternId": "E", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "J", "rotation": 180}, "BOTTOM": {"patternId": "I", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C131\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=I, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=J, rotation=180] [TOP: patternId=arrow_left, rotation=90] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=E, rotation=90]\n [BOTTOM: patternId=I, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=J, rotation=180\n- TOP: patternId=arrow_left, rotation=90\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=E, rotation=90\n- BOTTOM: patternId=I, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C131/initial_net.png", "targetTopFaceImage": "images/C131/target_top_face.png"}, "__sample_id__": "C131"} +{"taskType": "roll_to_target_top_face", "code": "C132", "name": "Goal Roll C132", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "W", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "I", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "H", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "smile", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "W", "rotation": 180}, "FRONT": {"patternId": "I", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "H", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "smile", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "smile", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C132/initial_net.png", "targetTopFaceImage": "../images/C132/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 4, "targetRotationOffset": 270, "levelId": 132, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-132.json"}, "rollSequence": ["S", "N", "N", "N"], "observedPathFaces": [{"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "N", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "W", "rotation": 180}, "FRONT": {"patternId": "I", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "H", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "smile", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C132\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=smile, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=H, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=W, rotation=180] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=I, rotation=180]\n [BOTTOM: patternId=smile, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=H, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=W, rotation=180\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=I, rotation=180\n- BOTTOM: patternId=smile, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C132/initial_net.png", "targetTopFaceImage": "images/C132/target_top_face.png"}, "__sample_id__": "C132"} +{"taskType": "roll_to_target_top_face", "code": "C133", "name": "Goal Roll C133", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "F", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "square", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "heart", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_right", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "F", "rotation": 90}, "FRONT": {"patternId": "square", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "heart", "rotation": 180}, "LEFT": {"patternId": "arrow_right", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "square", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C133/initial_net.png", "targetTopFaceImage": "../images/C133/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 3, "targetRotationOffset": 90, "levelId": 133, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-133.json"}, "rollSequence": ["S", "S", "S", "W"], "observedPathFaces": [{"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "F", "rotation": 90}, "FRONT": {"patternId": "square", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "heart", "rotation": 180}, "LEFT": {"patternId": "arrow_right", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C133\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=square, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=heart, rotation=180]\n[LEFT: patternId=arrow_right, rotation=180] [TOP: patternId=F, rotation=90] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=square, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=heart, rotation=180\n- LEFT: patternId=arrow_right, rotation=180\n- TOP: patternId=F, rotation=90\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=square, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C133/initial_net.png", "targetTopFaceImage": "images/C133/target_top_face.png"}, "__sample_id__": "C133"} +{"taskType": "roll_to_target_top_face", "code": "C134", "name": "Goal Roll C134", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "star", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "H", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Q", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "5", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "star", "rotation": 270}, "FRONT": {"patternId": "H", "rotation": 90}, "RIGHT": {"patternId": "Q", "rotation": 90}, "BACK": {"patternId": "5", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "H", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C134/initial_net.png", "targetTopFaceImage": "../images/C134/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 134, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-134.json"}, "rollSequence": ["N", "N", "N", "S", "E"], "observedPathFaces": [{"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "N", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "star", "rotation": 270}, "FRONT": {"patternId": "H", "rotation": 90}, "RIGHT": {"patternId": "Q", "rotation": 90}, "BACK": {"patternId": "5", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C134\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=H, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=5, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=star, rotation=270] [RIGHT: patternId=Q, rotation=90]\n [FRONT: patternId=H, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=5, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=star, rotation=270\n- RIGHT: patternId=Q, rotation=90\n- FRONT: patternId=H, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C134/initial_net.png", "targetTopFaceImage": "images/C134/target_top_face.png"}, "__sample_id__": "C134"} +{"taskType": "roll_to_target_top_face", "code": "C135", "name": "Goal Roll C135", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "9", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_down", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "T", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_up", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "9", "rotation": 270}, "RIGHT": {"patternId": "arrow_down", "rotation": 90}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "T", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C135/initial_net.png", "targetTopFaceImage": "../images/C135/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 2, "targetRotationOffset": 180, "levelId": 135, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-135.json"}, "rollSequence": ["E", "S", "W", "W"], "observedPathFaces": [{"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "9", "rotation": 270}, "RIGHT": {"patternId": "arrow_down", "rotation": 90}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C135\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=T, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=T, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=arrow_down, rotation=90]\n [FRONT: patternId=9, rotation=270]\n [BOTTOM: patternId=arrow_up, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=T, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=arrow_down, rotation=90\n- FRONT: patternId=9, rotation=270\n- BOTTOM: patternId=arrow_up, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C135/initial_net.png", "targetTopFaceImage": "images/C135/target_top_face.png"}, "__sample_id__": "C135"} +{"taskType": "roll_to_target_top_face", "code": "C136", "name": "Goal Roll C136", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "2", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "S", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_up", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "diamond", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "2", "rotation": 90}, "FRONT": {"patternId": "S", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_up", "rotation": 90}, "BOTTOM": {"patternId": "diamond", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "2", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C136/initial_net.png", "targetTopFaceImage": "../images/C136/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 2, "targetRotationOffset": 180, "levelId": 136, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-136.json"}, "rollSequence": ["S", "N", "W", "W"], "observedPathFaces": [{"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "N", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "2", "rotation": 90}, "FRONT": {"patternId": "S", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_up", "rotation": 90}, "BOTTOM": {"patternId": "diamond", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C136\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=2, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=arrow_up, rotation=90] [TOP: patternId=2, rotation=90] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=S, rotation=180]\n [BOTTOM: patternId=diamond, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=arrow_up, rotation=90\n- TOP: patternId=2, rotation=90\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=S, rotation=180\n- BOTTOM: patternId=diamond, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C136/initial_net.png", "targetTopFaceImage": "images/C136/target_top_face.png"}, "__sample_id__": "C136"} +{"taskType": "roll_to_target_top_face", "code": "C137", "name": "Goal Roll C137", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "arrow_left", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "B", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "7", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "arrow_left", "rotation": 0}, "FRONT": {"patternId": "B", "rotation": 90}, "RIGHT": {"patternId": "7", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "B", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C137/initial_net.png", "targetTopFaceImage": "../images/C137/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 137, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-137.json"}, "rollSequence": ["E", "E", "S", "N"], "observedPathFaces": [{"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "S", "N"]}, "legacy_answer": {"TOP": {"patternId": "arrow_left", "rotation": 0}, "FRONT": {"patternId": "B", "rotation": 90}, "RIGHT": {"patternId": "7", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C137\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=B, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=arrow_left, rotation=0] [RIGHT: patternId=7, rotation=180]\n [FRONT: patternId=B, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=arrow_left, rotation=0\n- RIGHT: patternId=7, rotation=180\n- FRONT: patternId=B, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C137/initial_net.png", "targetTopFaceImage": "images/C137/target_top_face.png"}, "__sample_id__": "C137"} +{"taskType": "roll_to_target_top_face", "code": "C138", "name": "Goal Roll C138", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "5", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "circle", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "4", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "5", "rotation": 90}, "BACK": {"patternId": "circle", "rotation": 180}, "LEFT": {"patternId": "4", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "5", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C138/initial_net.png", "targetTopFaceImage": "../images/C138/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 4, "targetRotationOffset": 270, "levelId": 138, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-138.json"}, "rollSequence": ["N", "E", "W", "W"], "observedPathFaces": [{"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "5", "rotation": 90}, "BACK": {"patternId": "circle", "rotation": 180}, "LEFT": {"patternId": "4", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C138\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=5, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=circle, rotation=180]\n[LEFT: patternId=4, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=5, rotation=90]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=circle, rotation=180\n- LEFT: patternId=4, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=5, rotation=90\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C138/initial_net.png", "targetTopFaceImage": "images/C138/target_top_face.png"}, "__sample_id__": "C138"} +{"taskType": "roll_to_target_top_face", "code": "C139", "name": "Goal Roll C139", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "S", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "smile", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "H", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "A", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "S", "rotation": 90}, "FRONT": {"patternId": "smile", "rotation": 180}, "RIGHT": {"patternId": "H", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "A", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "A", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C139/initial_net.png", "targetTopFaceImage": "../images/C139/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 4, "targetRotationOffset": 270, "levelId": 139, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-139.json"}, "rollSequence": ["S", "N", "E", "E"], "observedPathFaces": [{"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "N", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "S", "rotation": 90}, "FRONT": {"patternId": "smile", "rotation": 180}, "RIGHT": {"patternId": "H", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "A", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C139\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=A, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=S, rotation=90] [RIGHT: patternId=H, rotation=90]\n [FRONT: patternId=smile, rotation=180]\n [BOTTOM: patternId=A, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=S, rotation=90\n- RIGHT: patternId=H, rotation=90\n- FRONT: patternId=smile, rotation=180\n- BOTTOM: patternId=A, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C139/initial_net.png", "targetTopFaceImage": "images/C139/target_top_face.png"}, "__sample_id__": "C139"} +{"taskType": "roll_to_target_top_face", "code": "C140", "name": "Goal Roll C140", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "U", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "G", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "M", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "N", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "U", "rotation": 90}, "FRONT": {"patternId": "G", "rotation": 90}, "RIGHT": {"patternId": "M", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "N", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "N", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C140/initial_net.png", "targetTopFaceImage": "../images/C140/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 4, "targetRotationOffset": 180, "levelId": 140, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-140.json"}, "rollSequence": ["E", "W", "S", "S"], "observedPathFaces": [{"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "W", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "U", "rotation": 90}, "FRONT": {"patternId": "G", "rotation": 90}, "RIGHT": {"patternId": "M", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "N", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C140\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=N, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=U, rotation=90] [RIGHT: patternId=M, rotation=0]\n [FRONT: patternId=G, rotation=90]\n [BOTTOM: patternId=N, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=U, rotation=90\n- RIGHT: patternId=M, rotation=0\n- FRONT: patternId=G, rotation=90\n- BOTTOM: patternId=N, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C140/initial_net.png", "targetTopFaceImage": "images/C140/target_top_face.png"}, "__sample_id__": "C140"} +{"taskType": "roll_to_target_top_face", "code": "C141", "name": "Goal Roll C141", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "arrow_left", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "6", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "D", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "C", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "arrow_left", "rotation": 180}, "RIGHT": {"patternId": "6", "rotation": 270}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "C", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "arrow_left", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C141/initial_net.png", "targetTopFaceImage": "../images/C141/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 141, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-141.json"}, "rollSequence": ["N", "E", "S", "E"], "observedPathFaces": [{"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "arrow_left", "rotation": 180}, "RIGHT": {"patternId": "6", "rotation": 270}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "C", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C141\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=arrow_left, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=D, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=6, rotation=270]\n [FRONT: patternId=arrow_left, rotation=180]\n [BOTTOM: patternId=C, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=D, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=6, rotation=270\n- FRONT: patternId=arrow_left, rotation=180\n- BOTTOM: patternId=C, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C141/initial_net.png", "targetTopFaceImage": "images/C141/target_top_face.png"}, "__sample_id__": "C141"} +{"taskType": "roll_to_target_top_face", "code": "C142", "name": "Goal Roll C142", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "V", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "I", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_down", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "X", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "V", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 270}, "LEFT": {"patternId": "arrow_down", "rotation": 0}, "BOTTOM": {"patternId": "X", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "X", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C142/initial_net.png", "targetTopFaceImage": "../images/C142/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 3, "targetRotationOffset": 270, "levelId": 142, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-142.json"}, "rollSequence": ["W", "N", "W", "E", "E"], "observedPathFaces": [{"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "W", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "V", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 270}, "LEFT": {"patternId": "arrow_down", "rotation": 0}, "BOTTOM": {"patternId": "X", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C142\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=X, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=I, rotation=270]\n[LEFT: patternId=arrow_down, rotation=0] [TOP: patternId=V, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=X, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=I, rotation=270\n- LEFT: patternId=arrow_down, rotation=0\n- TOP: patternId=V, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=X, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C142/initial_net.png", "targetTopFaceImage": "images/C142/target_top_face.png"}, "__sample_id__": "C142"} +{"taskType": "roll_to_target_top_face", "code": "C143", "name": "Goal Roll C143", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "star", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "L", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "J", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "star", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "L", "rotation": 180}, "BACK": {"patternId": "J", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "J", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C143/initial_net.png", "targetTopFaceImage": "../images/C143/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 143, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-143.json"}, "rollSequence": ["N", "E", "W", "N"], "observedPathFaces": [{"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "star", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "L", "rotation": 180}, "BACK": {"patternId": "J", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C143\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=J, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=J, rotation=90]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=star, rotation=180] [RIGHT: patternId=L, rotation=180]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=J, rotation=90\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=star, rotation=180\n- RIGHT: patternId=L, rotation=180\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C143/initial_net.png", "targetTopFaceImage": "images/C143/target_top_face.png"}, "__sample_id__": "C143"} +{"taskType": "roll_to_target_top_face", "code": "C144", "name": "Goal Roll C144", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "L", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "I", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "K", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "L", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "8", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "L", "rotation": 90}, "FRONT": {"patternId": "I", "rotation": 270}, "RIGHT": {"patternId": "K", "rotation": 180}, "BACK": {"patternId": "L", "rotation": 90}, "LEFT": {"patternId": "8", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "I", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C144/initial_net.png", "targetTopFaceImage": "../images/C144/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 144, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-144.json"}, "rollSequence": ["N", "W", "N", "N", "W"], "observedPathFaces": [{"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "N", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "L", "rotation": 90}, "FRONT": {"patternId": "I", "rotation": 270}, "RIGHT": {"patternId": "K", "rotation": 180}, "BACK": {"patternId": "L", "rotation": 90}, "LEFT": {"patternId": "8", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C144\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=I, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=L, rotation=90]\n[LEFT: patternId=8, rotation=0] [TOP: patternId=L, rotation=90] [RIGHT: patternId=K, rotation=180]\n [FRONT: patternId=I, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=L, rotation=90\n- LEFT: patternId=8, rotation=0\n- TOP: patternId=L, rotation=90\n- RIGHT: patternId=K, rotation=180\n- FRONT: patternId=I, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C144/initial_net.png", "targetTopFaceImage": "images/C144/target_top_face.png"}, "__sample_id__": "C144"} +{"taskType": "roll_to_target_top_face", "code": "C145", "name": "Goal Roll C145", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "X", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "K", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "A", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "X", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "K", "rotation": 90}, "BACK": {"patternId": "A", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "A", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C145/initial_net.png", "targetTopFaceImage": "../images/C145/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 145, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-145.json"}, "rollSequence": ["N", "N", "E", "W", "S"], "observedPathFaces": [{"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "E", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "X", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "K", "rotation": 90}, "BACK": {"patternId": "A", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C145\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=A, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=A, rotation=90]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=X, rotation=270] [RIGHT: patternId=K, rotation=90]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=A, rotation=90\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=X, rotation=270\n- RIGHT: patternId=K, rotation=90\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C145/initial_net.png", "targetTopFaceImage": "images/C145/target_top_face.png"}, "__sample_id__": "C145"} +{"taskType": "roll_to_target_top_face", "code": "C146", "name": "Goal Roll C146", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "V", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "Y", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "H", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "L", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "B", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "V", "rotation": 270}, "FRONT": {"patternId": "Y", "rotation": 0}, "RIGHT": {"patternId": "H", "rotation": 270}, "BACK": {"patternId": "L", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "B", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "B", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C146/initial_net.png", "targetTopFaceImage": "../images/C146/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 5, "targetRotationOffset": 180, "levelId": 146, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-146.json"}, "rollSequence": ["E", "N", "W", "W", "W"], "observedPathFaces": [{"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "W", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "V", "rotation": 270}, "FRONT": {"patternId": "Y", "rotation": 0}, "RIGHT": {"patternId": "H", "rotation": 270}, "BACK": {"patternId": "L", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "B", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C146\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=B, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=L, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=V, rotation=270] [RIGHT: patternId=H, rotation=270]\n [FRONT: patternId=Y, rotation=0]\n [BOTTOM: patternId=B, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=L, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=V, rotation=270\n- RIGHT: patternId=H, rotation=270\n- FRONT: patternId=Y, rotation=0\n- BOTTOM: patternId=B, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C146/initial_net.png", "targetTopFaceImage": "images/C146/target_top_face.png"}, "__sample_id__": "C146"} +{"taskType": "roll_to_target_top_face", "code": "C147", "name": "Goal Roll C147", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "T", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "R", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "W", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "T", "rotation": 0}, "RIGHT": {"patternId": "R", "rotation": 180}, "BACK": {"patternId": "W", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "T", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C147/initial_net.png", "targetTopFaceImage": "../images/C147/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 5, "targetRotationOffset": 90, "levelId": 147, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-147.json"}, "rollSequence": ["N", "E", "E", "W", "W"], "observedPathFaces": [{"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "E", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "T", "rotation": 0}, "RIGHT": {"patternId": "R", "rotation": 180}, "BACK": {"patternId": "W", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C147\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=T, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=W, rotation=90]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=R, rotation=180]\n [FRONT: patternId=T, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=W, rotation=90\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=R, rotation=180\n- FRONT: patternId=T, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C147/initial_net.png", "targetTopFaceImage": "images/C147/target_top_face.png"}, "__sample_id__": "C147"} +{"taskType": "roll_to_target_top_face", "code": "C148", "name": "Goal Roll C148", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "star", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "M", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "2", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "7", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "star", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 180}, "LEFT": {"patternId": "2", "rotation": 180}, "BOTTOM": {"patternId": "7", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "7", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C148/initial_net.png", "targetTopFaceImage": "../images/C148/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 2, "targetRotationOffset": 270, "levelId": 148, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-148.json"}, "rollSequence": ["W", "W", "N", "N", "S"], "observedPathFaces": [{"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "N", "N", "S"]}, "legacy_answer": {"TOP": {"patternId": "star", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 180}, "LEFT": {"patternId": "2", "rotation": 180}, "BOTTOM": {"patternId": "7", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C148\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=7, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=M, rotation=180]\n[LEFT: patternId=2, rotation=180] [TOP: patternId=star, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=7, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=M, rotation=180\n- LEFT: patternId=2, rotation=180\n- TOP: patternId=star, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=7, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C148/initial_net.png", "targetTopFaceImage": "images/C148/target_top_face.png"}, "__sample_id__": "C148"} +{"taskType": "roll_to_target_top_face", "code": "C149", "name": "Goal Roll C149", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "triangle", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "R", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "star", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "diamond", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "B", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "triangle", "rotation": 180}, "FRONT": {"patternId": "R", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 90}, "LEFT": {"patternId": "diamond", "rotation": 180}, "BOTTOM": {"patternId": "B", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "R", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C149/initial_net.png", "targetTopFaceImage": "../images/C149/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 149, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-149.json"}, "rollSequence": ["N", "S", "S", "W", "S"], "observedPathFaces": [{"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "S", "S", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "triangle", "rotation": 180}, "FRONT": {"patternId": "R", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 90}, "LEFT": {"patternId": "diamond", "rotation": 180}, "BOTTOM": {"patternId": "B", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C149\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=R, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=star, rotation=90]\n[LEFT: patternId=diamond, rotation=180] [TOP: patternId=triangle, rotation=180] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=R, rotation=0]\n [BOTTOM: patternId=B, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=star, rotation=90\n- LEFT: patternId=diamond, rotation=180\n- TOP: patternId=triangle, rotation=180\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=R, rotation=0\n- BOTTOM: patternId=B, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C149/initial_net.png", "targetTopFaceImage": "images/C149/target_top_face.png"}, "__sample_id__": "C149"} +{"taskType": "roll_to_target_top_face", "code": "C150", "name": "Goal Roll C150", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "I", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "N", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "2", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "P", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "Y", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "I", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "2", "rotation": 270}, "LEFT": {"patternId": "P", "rotation": 90}, "BOTTOM": {"patternId": "Y", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "Y", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C150/initial_net.png", "targetTopFaceImage": "../images/C150/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 3, "targetRotationOffset": 270, "levelId": 150, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-150.json"}, "rollSequence": ["W", "N", "W", "W", "W"], "observedPathFaces": [{"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "W", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "I", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "2", "rotation": 270}, "LEFT": {"patternId": "P", "rotation": 90}, "BOTTOM": {"patternId": "Y", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C150\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=Y, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=2, rotation=270]\n[LEFT: patternId=P, rotation=90] [TOP: patternId=I, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=N, rotation=180]\n [BOTTOM: patternId=Y, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=2, rotation=270\n- LEFT: patternId=P, rotation=90\n- TOP: patternId=I, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=N, rotation=180\n- BOTTOM: patternId=Y, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C150/initial_net.png", "targetTopFaceImage": "images/C150/target_top_face.png"}, "__sample_id__": "C150"} +{"taskType": "roll_to_target_top_face", "code": "C151", "name": "Goal Roll C151", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "Y", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "star", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_up", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "Y", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 270}, "LEFT": {"patternId": "arrow_up", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "star", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C151/initial_net.png", "targetTopFaceImage": "../images/C151/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 151, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-151.json"}, "rollSequence": ["N", "W", "E", "N"], "observedPathFaces": [{"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "Y", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 270}, "LEFT": {"patternId": "arrow_up", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C151\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=star, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=star, rotation=270]\n[LEFT: patternId=arrow_up, rotation=270] [TOP: patternId=Y, rotation=180] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=star, rotation=270\n- LEFT: patternId=arrow_up, rotation=270\n- TOP: patternId=Y, rotation=180\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C151/initial_net.png", "targetTopFaceImage": "images/C151/target_top_face.png"}, "__sample_id__": "C151"} +{"taskType": "roll_to_target_top_face", "code": "C152", "name": "Goal Roll C152", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "heart", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "U", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "6", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "U", "rotation": 90}, "BOTTOM": {"patternId": "6", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "heart", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C152/initial_net.png", "targetTopFaceImage": "../images/C152/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 152, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-152.json"}, "rollSequence": ["W", "S", "E", "W", "N"], "observedPathFaces": [{"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "E", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "U", "rotation": 90}, "BOTTOM": {"patternId": "6", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C152\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=heart, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=U, rotation=90] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=heart, rotation=270]\n [BOTTOM: patternId=6, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=U, rotation=90\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=heart, rotation=270\n- BOTTOM: patternId=6, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C152/initial_net.png", "targetTopFaceImage": "images/C152/target_top_face.png"}, "__sample_id__": "C152"} +{"taskType": "roll_to_target_top_face", "code": "C153", "name": "Goal Roll C153", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "P", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "V", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "C", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "P", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "V", "rotation": 90}, "BACK": {"patternId": "C", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "C", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C153/initial_net.png", "targetTopFaceImage": "../images/C153/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 153, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-153.json"}, "rollSequence": ["E", "N", "E", "S"], "observedPathFaces": [{"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "P", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "V", "rotation": 90}, "BACK": {"patternId": "C", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C153\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=C, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=C, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=P, rotation=180] [RIGHT: patternId=V, rotation=90]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=C, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=P, rotation=180\n- RIGHT: patternId=V, rotation=90\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C153/initial_net.png", "targetTopFaceImage": "images/C153/target_top_face.png"}, "__sample_id__": "C153"} +{"taskType": "roll_to_target_top_face", "code": "C154", "name": "Goal Roll C154", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "V", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "7", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "K", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "V", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "K", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "7", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C154/initial_net.png", "targetTopFaceImage": "../images/C154/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 154, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-154.json"}, "rollSequence": ["W", "S", "W", "E"], "observedPathFaces": [{"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "W", "E"]}, "legacy_answer": {"TOP": {"patternId": "V", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "K", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C154\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=7, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=K, rotation=0] [TOP: patternId=V, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=7, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=K, rotation=0\n- TOP: patternId=V, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=7, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C154/initial_net.png", "targetTopFaceImage": "images/C154/target_top_face.png"}, "__sample_id__": "C154"} +{"taskType": "roll_to_target_top_face", "code": "C155", "name": "Goal Roll C155", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "A", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Y", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "Y", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "X", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "A", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Y", "rotation": 90}, "BACK": {"patternId": "Y", "rotation": 90}, "LEFT": {"patternId": "X", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "X", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C155/initial_net.png", "targetTopFaceImage": "../images/C155/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 5, "targetRotationOffset": 90, "levelId": 155, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-155.json"}, "rollSequence": ["E", "N", "N", "E", "E"], "observedPathFaces": [{"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "N", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "A", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Y", "rotation": 90}, "BACK": {"patternId": "Y", "rotation": 90}, "LEFT": {"patternId": "X", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C155\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=X, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=Y, rotation=90]\n[LEFT: patternId=X, rotation=90] [TOP: patternId=A, rotation=270] [RIGHT: patternId=Y, rotation=90]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Y, rotation=90\n- LEFT: patternId=X, rotation=90\n- TOP: patternId=A, rotation=270\n- RIGHT: patternId=Y, rotation=90\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C155/initial_net.png", "targetTopFaceImage": "images/C155/target_top_face.png"}, "__sample_id__": "C155"} +{"taskType": "roll_to_target_top_face", "code": "C156", "name": "Goal Roll C156", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "8", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Q", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "C", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "heart", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "8", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Q", "rotation": 90}, "BACK": {"patternId": "C", "rotation": 180}, "LEFT": {"patternId": "heart", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "heart", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C156/initial_net.png", "targetTopFaceImage": "../images/C156/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 156, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-156.json"}, "rollSequence": ["E", "N", "E", "N"], "observedPathFaces": [{"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "8", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Q", "rotation": 90}, "BACK": {"patternId": "C", "rotation": 180}, "LEFT": {"patternId": "heart", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C156\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=heart, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=C, rotation=180]\n[LEFT: patternId=heart, rotation=180] [TOP: patternId=8, rotation=180] [RIGHT: patternId=Q, rotation=90]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=C, rotation=180\n- LEFT: patternId=heart, rotation=180\n- TOP: patternId=8, rotation=180\n- RIGHT: patternId=Q, rotation=90\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C156/initial_net.png", "targetTopFaceImage": "images/C156/target_top_face.png"}, "__sample_id__": "C156"} +{"taskType": "roll_to_target_top_face", "code": "C157", "name": "Goal Roll C157", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "arrow_down", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "R", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "R", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "6", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "arrow_down", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "R", "rotation": 180}, "BACK": {"patternId": "R", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "arrow_down", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C157/initial_net.png", "targetTopFaceImage": "../images/C157/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 2, "targetRotationOffset": 180, "levelId": 157, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-157.json"}, "rollSequence": ["E", "W", "N", "N"], "observedPathFaces": [{"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "W", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "arrow_down", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "R", "rotation": 180}, "BACK": {"patternId": "R", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C157\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=arrow_down, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=R, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=arrow_down, rotation=270] [RIGHT: patternId=R, rotation=180]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=6, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=R, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=arrow_down, rotation=270\n- RIGHT: patternId=R, rotation=180\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=6, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C157/initial_net.png", "targetTopFaceImage": "images/C157/target_top_face.png"}, "__sample_id__": "C157"} +{"taskType": "roll_to_target_top_face", "code": "C158", "name": "Goal Roll C158", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "5", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "K", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "9", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "5", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "9", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "K", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C158/initial_net.png", "targetTopFaceImage": "../images/C158/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 158, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-158.json"}, "rollSequence": ["N", "N", "S", "W"], "observedPathFaces": [{"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "5", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "9", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C158\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=K, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=K, rotation=270]\n[LEFT: patternId=9, rotation=90] [TOP: patternId=5, rotation=270] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=K, rotation=270\n- LEFT: patternId=9, rotation=90\n- TOP: patternId=5, rotation=270\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C158/initial_net.png", "targetTopFaceImage": "images/C158/target_top_face.png"}, "__sample_id__": "C158"} +{"taskType": "roll_to_target_top_face", "code": "C159", "name": "Goal Roll C159", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "7", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "2", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "circle", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "star", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 0}, "RIGHT": {"patternId": "2", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 0}, "LEFT": {"patternId": "star", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "7", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C159/initial_net.png", "targetTopFaceImage": "../images/C159/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 2, "targetRotationOffset": 270, "levelId": 159, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-159.json"}, "rollSequence": ["W", "N", "N", "N", "S"], "observedPathFaces": [{"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "N", "N", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 0}, "RIGHT": {"patternId": "2", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 0}, "LEFT": {"patternId": "star", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C159\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=7, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=circle, rotation=0]\n[LEFT: patternId=star, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=2, rotation=0]\n [FRONT: patternId=7, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=circle, rotation=0\n- LEFT: patternId=star, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=2, rotation=0\n- FRONT: patternId=7, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C159/initial_net.png", "targetTopFaceImage": "images/C159/target_top_face.png"}, "__sample_id__": "C159"} +{"taskType": "roll_to_target_top_face", "code": "C160", "name": "Goal Roll C160", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "D", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "V", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "O", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "Q", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "O", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "D", "rotation": 270}, "FRONT": {"patternId": "V", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "O", "rotation": 0}, "LEFT": {"patternId": "Q", "rotation": 180}, "BOTTOM": {"patternId": "O", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "V", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C160/initial_net.png", "targetTopFaceImage": "../images/C160/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 4, "targetRotationOffset": 270, "levelId": 160, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-160.json"}, "rollSequence": ["W", "S", "E", "E", "E"], "observedPathFaces": [{"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "E", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "D", "rotation": 270}, "FRONT": {"patternId": "V", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "O", "rotation": 0}, "LEFT": {"patternId": "Q", "rotation": 180}, "BOTTOM": {"patternId": "O", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C160\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=V, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=O, rotation=0]\n[LEFT: patternId=Q, rotation=180] [TOP: patternId=D, rotation=270] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=V, rotation=180]\n [BOTTOM: patternId=O, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=O, rotation=0\n- LEFT: patternId=Q, rotation=180\n- TOP: patternId=D, rotation=270\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=V, rotation=180\n- BOTTOM: patternId=O, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C160/initial_net.png", "targetTopFaceImage": "images/C160/target_top_face.png"}, "__sample_id__": "C160"} +{"taskType": "roll_to_target_top_face", "code": "C161", "name": "Goal Roll C161", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "Y", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "3", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "W", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "Y", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "3", "rotation": 180}, "BACK": {"patternId": "W", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "W", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C161/initial_net.png", "targetTopFaceImage": "../images/C161/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 161, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-161.json"}, "rollSequence": ["N", "E", "W", "N", "E"], "observedPathFaces": [{"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "W", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "Y", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "3", "rotation": 180}, "BACK": {"patternId": "W", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C161\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=W, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=W, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=Y, rotation=180] [RIGHT: patternId=3, rotation=180]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=W, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=Y, rotation=180\n- RIGHT: patternId=3, rotation=180\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C161/initial_net.png", "targetTopFaceImage": "images/C161/target_top_face.png"}, "__sample_id__": "C161"} +{"taskType": "roll_to_target_top_face", "code": "C162", "name": "Goal Roll C162", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "Y", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "V", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_left", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_left", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "I", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "Y", "rotation": 180}, "FRONT": {"patternId": "V", "rotation": 180}, "RIGHT": {"patternId": "arrow_left", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_left", "rotation": 270}, "BOTTOM": {"patternId": "I", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "arrow_left", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C162/initial_net.png", "targetTopFaceImage": "../images/C162/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 162, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-162.json"}, "rollSequence": ["E", "E", "S", "E", "S"], "observedPathFaces": [{"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "S", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "Y", "rotation": 180}, "FRONT": {"patternId": "V", "rotation": 180}, "RIGHT": {"patternId": "arrow_left", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_left", "rotation": 270}, "BOTTOM": {"patternId": "I", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C162\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=arrow_left, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=arrow_left, rotation=270] [TOP: patternId=Y, rotation=180] [RIGHT: patternId=arrow_left, rotation=90]\n [FRONT: patternId=V, rotation=180]\n [BOTTOM: patternId=I, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=arrow_left, rotation=270\n- TOP: patternId=Y, rotation=180\n- RIGHT: patternId=arrow_left, rotation=90\n- FRONT: patternId=V, rotation=180\n- BOTTOM: patternId=I, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C162/initial_net.png", "targetTopFaceImage": "images/C162/target_top_face.png"}, "__sample_id__": "C162"} +{"taskType": "roll_to_target_top_face", "code": "C163", "name": "Goal Roll C163", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "smile", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "S", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "diamond", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "G", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "smile", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 0}, "BACK": {"patternId": "diamond", "rotation": 90}, "LEFT": {"patternId": "G", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "S", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C163/initial_net.png", "targetTopFaceImage": "../images/C163/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 2, "targetRotationOffset": 180, "levelId": 163, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-163.json"}, "rollSequence": ["N", "W", "N", "N"], "observedPathFaces": [{"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "smile", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 0}, "BACK": {"patternId": "diamond", "rotation": 90}, "LEFT": {"patternId": "G", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C163\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=S, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=diamond, rotation=90]\n[LEFT: patternId=G, rotation=0] [TOP: patternId=smile, rotation=180] [RIGHT: patternId=S, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=diamond, rotation=90\n- LEFT: patternId=G, rotation=0\n- TOP: patternId=smile, rotation=180\n- RIGHT: patternId=S, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C163/initial_net.png", "targetTopFaceImage": "images/C163/target_top_face.png"}, "__sample_id__": "C163"} +{"taskType": "roll_to_target_top_face", "code": "C164", "name": "Goal Roll C164", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "P", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "Q", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "D", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "P", "rotation": 270}, "FRONT": {"patternId": "Q", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "D", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "Q", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C164/initial_net.png", "targetTopFaceImage": "../images/C164/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 164, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-164.json"}, "rollSequence": ["W", "S", "W", "E"], "observedPathFaces": [{"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "W", "E"]}, "legacy_answer": {"TOP": {"patternId": "P", "rotation": 270}, "FRONT": {"patternId": "Q", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "D", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C164\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=Q, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=D, rotation=270] [TOP: patternId=P, rotation=270] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=Q, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=D, rotation=270\n- TOP: patternId=P, rotation=270\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=Q, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C164/initial_net.png", "targetTopFaceImage": "images/C164/target_top_face.png"}, "__sample_id__": "C164"} +{"taskType": "roll_to_target_top_face", "code": "C165", "name": "Goal Roll C165", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "2", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "M", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "A", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "star", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 270}, "RIGHT": {"patternId": "M", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "A", "rotation": 270}, "BOTTOM": {"patternId": "star", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "A", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C165/initial_net.png", "targetTopFaceImage": "../images/C165/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 165, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-165.json"}, "rollSequence": ["E", "S", "W", "S"], "observedPathFaces": [{"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 270}, "RIGHT": {"patternId": "M", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "A", "rotation": 270}, "BOTTOM": {"patternId": "star", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C165\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=A, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=A, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=M, rotation=0]\n [FRONT: patternId=2, rotation=270]\n [BOTTOM: patternId=star, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=A, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=M, rotation=0\n- FRONT: patternId=2, rotation=270\n- BOTTOM: patternId=star, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C165/initial_net.png", "targetTopFaceImage": "images/C165/target_top_face.png"}, "__sample_id__": "C165"} +{"taskType": "roll_to_target_top_face", "code": "C166", "name": "Goal Roll C166", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "circle", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "diamond", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "smile", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_up", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "Q", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "circle", "rotation": 270}, "FRONT": {"patternId": "diamond", "rotation": 0}, "RIGHT": {"patternId": "smile", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_up", "rotation": 90}, "BOTTOM": {"patternId": "Q", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "Q", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C166/initial_net.png", "targetTopFaceImage": "../images/C166/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 5, "targetRotationOffset": 270, "levelId": 166, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-166.json"}, "rollSequence": ["E", "S", "W", "S", "S"], "observedPathFaces": [{"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "W", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "circle", "rotation": 270}, "FRONT": {"patternId": "diamond", "rotation": 0}, "RIGHT": {"patternId": "smile", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_up", "rotation": 90}, "BOTTOM": {"patternId": "Q", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C166\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=Q, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=arrow_up, rotation=90] [TOP: patternId=circle, rotation=270] [RIGHT: patternId=smile, rotation=90]\n [FRONT: patternId=diamond, rotation=0]\n [BOTTOM: patternId=Q, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=arrow_up, rotation=90\n- TOP: patternId=circle, rotation=270\n- RIGHT: patternId=smile, rotation=90\n- FRONT: patternId=diamond, rotation=0\n- BOTTOM: patternId=Q, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C166/initial_net.png", "targetTopFaceImage": "images/C166/target_top_face.png"}, "__sample_id__": "C166"} +{"taskType": "roll_to_target_top_face", "code": "C167", "name": "Goal Roll C167", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "O", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "8", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "B", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "S", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "O", "rotation": 90}, "FRONT": {"patternId": "8", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 0}, "LEFT": {"patternId": "S", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "8", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C167/initial_net.png", "targetTopFaceImage": "../images/C167/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 4, "targetRotationOffset": 270, "levelId": 167, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-167.json"}, "rollSequence": ["S", "S", "W", "S"], "observedPathFaces": [{"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 90}, "FRONT": {"patternId": "8", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 0}, "LEFT": {"patternId": "S", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C167\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=8, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=B, rotation=0]\n[LEFT: patternId=S, rotation=0] [TOP: patternId=O, rotation=90] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=8, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=B, rotation=0\n- LEFT: patternId=S, rotation=0\n- TOP: patternId=O, rotation=90\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=8, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C167/initial_net.png", "targetTopFaceImage": "images/C167/target_top_face.png"}, "__sample_id__": "C167"} +{"taskType": "roll_to_target_top_face", "code": "C168", "name": "Goal Roll C168", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "7", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "V", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "8", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "7", "rotation": 0}, "FRONT": {"patternId": "V", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "V", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C168/initial_net.png", "targetTopFaceImage": "../images/C168/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 168, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-168.json"}, "rollSequence": ["W", "W", "E", "S"], "observedPathFaces": [{"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "7", "rotation": 0}, "FRONT": {"patternId": "V", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C168\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=V, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=8, rotation=0] [TOP: patternId=7, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=V, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=8, rotation=0\n- TOP: patternId=7, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=V, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C168/initial_net.png", "targetTopFaceImage": "images/C168/target_top_face.png"}, "__sample_id__": "C168"} +{"taskType": "roll_to_target_top_face", "code": "C169", "name": "Goal Roll C169", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "D", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "Q", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "4", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "M", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "D", "rotation": 90}, "FRONT": {"patternId": "Q", "rotation": 180}, "RIGHT": {"patternId": "4", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "M", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "4", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C169/initial_net.png", "targetTopFaceImage": "../images/C169/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 169, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-169.json"}, "rollSequence": ["W", "W", "W", "S"], "observedPathFaces": [{"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "D", "rotation": 90}, "FRONT": {"patternId": "Q", "rotation": 180}, "RIGHT": {"patternId": "4", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "M", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C169\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=4, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=M, rotation=180] [TOP: patternId=D, rotation=90] [RIGHT: patternId=4, rotation=0]\n [FRONT: patternId=Q, rotation=180]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=M, rotation=180\n- TOP: patternId=D, rotation=90\n- RIGHT: patternId=4, rotation=0\n- FRONT: patternId=Q, rotation=180\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C169/initial_net.png", "targetTopFaceImage": "images/C169/target_top_face.png"}, "__sample_id__": "C169"} +{"taskType": "roll_to_target_top_face", "code": "C170", "name": "Goal Roll C170", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "B", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "G", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "3", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "4", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "B", "rotation": 0}, "BACK": {"patternId": "G", "rotation": 180}, "LEFT": {"patternId": "3", "rotation": 90}, "BOTTOM": {"patternId": "4", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "3", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C170/initial_net.png", "targetTopFaceImage": "../images/C170/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 2, "targetRotationOffset": 90, "levelId": 170, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-170.json"}, "rollSequence": ["N", "E", "S", "S"], "observedPathFaces": [{"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "B", "rotation": 0}, "BACK": {"patternId": "G", "rotation": 180}, "LEFT": {"patternId": "3", "rotation": 90}, "BOTTOM": {"patternId": "4", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C170\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=3, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=G, rotation=180]\n[LEFT: patternId=3, rotation=90] [TOP: patternId=?, rotation=0] [RIGHT: patternId=B, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=4, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=G, rotation=180\n- LEFT: patternId=3, rotation=90\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=B, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=4, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C170/initial_net.png", "targetTopFaceImage": "images/C170/target_top_face.png"}, "__sample_id__": "C170"} +{"taskType": "roll_to_target_top_face", "code": "C171", "name": "Goal Roll C171", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "E", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "H", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "5", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "E", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "E", "rotation": 90}, "FRONT": {"patternId": "H", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "5", "rotation": 180}, "BOTTOM": {"patternId": "E", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "E", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C171/initial_net.png", "targetTopFaceImage": "../images/C171/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 5, "targetRotationOffset": 180, "levelId": 171, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-171.json"}, "rollSequence": ["W", "S", "W", "E", "E"], "observedPathFaces": [{"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "W", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "E", "rotation": 90}, "FRONT": {"patternId": "H", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "5", "rotation": 180}, "BOTTOM": {"patternId": "E", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C171\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=E, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=5, rotation=180] [TOP: patternId=E, rotation=90] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=H, rotation=270]\n [BOTTOM: patternId=E, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=5, rotation=180\n- TOP: patternId=E, rotation=90\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=H, rotation=270\n- BOTTOM: patternId=E, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C171/initial_net.png", "targetTopFaceImage": "images/C171/target_top_face.png"}, "__sample_id__": "C171"} +{"taskType": "roll_to_target_top_face", "code": "C172", "name": "Goal Roll C172", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "L", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "I", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "K", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "M", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "L", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 270}, "BACK": {"patternId": "K", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "M", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "M", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C172/initial_net.png", "targetTopFaceImage": "../images/C172/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 2, "targetRotationOffset": 90, "levelId": 172, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-172.json"}, "rollSequence": ["N", "N", "E", "E", "S"], "observedPathFaces": [{"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "E", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "L", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 270}, "BACK": {"patternId": "K", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "M", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C172\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=M, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=K, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=L, rotation=180] [RIGHT: patternId=I, rotation=270]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=M, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=K, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=L, rotation=180\n- RIGHT: patternId=I, rotation=270\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=M, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C172/initial_net.png", "targetTopFaceImage": "images/C172/target_top_face.png"}, "__sample_id__": "C172"} +{"taskType": "roll_to_target_top_face", "code": "C173", "name": "Goal Roll C173", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "I", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "J", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "7", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "E", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "I", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "J", "rotation": 90}, "BACK": {"patternId": "7", "rotation": 270}, "LEFT": {"patternId": "E", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "E", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C173/initial_net.png", "targetTopFaceImage": "../images/C173/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 173, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-173.json"}, "rollSequence": ["E", "E", "N", "E"], "observedPathFaces": [{"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "I", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "J", "rotation": 90}, "BACK": {"patternId": "7", "rotation": 270}, "LEFT": {"patternId": "E", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C173\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=E, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=7, rotation=270]\n[LEFT: patternId=E, rotation=0] [TOP: patternId=I, rotation=90] [RIGHT: patternId=J, rotation=90]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=7, rotation=270\n- LEFT: patternId=E, rotation=0\n- TOP: patternId=I, rotation=90\n- RIGHT: patternId=J, rotation=90\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C173/initial_net.png", "targetTopFaceImage": "images/C173/target_top_face.png"}, "__sample_id__": "C173"} +{"taskType": "roll_to_target_top_face", "code": "C174", "name": "Goal Roll C174", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "P", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "R", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "E", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "Z", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "P", "rotation": 0}, "FRONT": {"patternId": "R", "rotation": 180}, "RIGHT": {"patternId": "E", "rotation": 90}, "BACK": {"patternId": "Z", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "R", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C174/initial_net.png", "targetTopFaceImage": "../images/C174/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 174, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-174.json"}, "rollSequence": ["N", "N", "N", "E", "E"], "observedPathFaces": [{"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "N", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "P", "rotation": 0}, "FRONT": {"patternId": "R", "rotation": 180}, "RIGHT": {"patternId": "E", "rotation": 90}, "BACK": {"patternId": "Z", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C174\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=R, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=Z, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=P, rotation=0] [RIGHT: patternId=E, rotation=90]\n [FRONT: patternId=R, rotation=180]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Z, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=P, rotation=0\n- RIGHT: patternId=E, rotation=90\n- FRONT: patternId=R, rotation=180\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C174/initial_net.png", "targetTopFaceImage": "images/C174/target_top_face.png"}, "__sample_id__": "C174"} +{"taskType": "roll_to_target_top_face", "code": "C175", "name": "Goal Roll C175", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "diamond", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "P", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "5", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "H", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "diamond", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "P", "rotation": 270}, "LEFT": {"patternId": "5", "rotation": 90}, "BOTTOM": {"patternId": "H", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "P", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C175/initial_net.png", "targetTopFaceImage": "../images/C175/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 175, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-175.json"}, "rollSequence": ["S", "W", "W", "E", "N"], "observedPathFaces": [{"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "W", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "diamond", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "P", "rotation": 270}, "LEFT": {"patternId": "5", "rotation": 90}, "BOTTOM": {"patternId": "H", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C175\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=P, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=P, rotation=270]\n[LEFT: patternId=5, rotation=90] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=diamond, rotation=270]\n [BOTTOM: patternId=H, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=P, rotation=270\n- LEFT: patternId=5, rotation=90\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=diamond, rotation=270\n- BOTTOM: patternId=H, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C175/initial_net.png", "targetTopFaceImage": "images/C175/target_top_face.png"}, "__sample_id__": "C175"} +{"taskType": "roll_to_target_top_face", "code": "C176", "name": "Goal Roll C176", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "1", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "E", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "F", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "O", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "1", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "E", "rotation": 90}, "LEFT": {"patternId": "F", "rotation": 0}, "BOTTOM": {"patternId": "O", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "E", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C176/initial_net.png", "targetTopFaceImage": "../images/C176/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 2, "targetRotationOffset": 90, "levelId": 176, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-176.json"}, "rollSequence": ["W", "S", "E", "E", "N"], "observedPathFaces": [{"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "E", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "1", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "E", "rotation": 90}, "LEFT": {"patternId": "F", "rotation": 0}, "BOTTOM": {"patternId": "O", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C176\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=E, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=E, rotation=90]\n[LEFT: patternId=F, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=1, rotation=0]\n [BOTTOM: patternId=O, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=E, rotation=90\n- LEFT: patternId=F, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=1, rotation=0\n- BOTTOM: patternId=O, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C176/initial_net.png", "targetTopFaceImage": "images/C176/target_top_face.png"}, "__sample_id__": "C176"} +{"taskType": "roll_to_target_top_face", "code": "C177", "name": "Goal Roll C177", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_right", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "star", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "W", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 270}, "BACK": {"patternId": "star", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "W", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "star", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C177/initial_net.png", "targetTopFaceImage": "../images/C177/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 177, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-177.json"}, "rollSequence": ["N", "S", "E", "N"], "observedPathFaces": [{"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "S", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 270}, "BACK": {"patternId": "star", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "W", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C177\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=star, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=star, rotation=270]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=arrow_right, rotation=270]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=W, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=star, rotation=270\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=arrow_right, rotation=270\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=W, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C177/initial_net.png", "targetTopFaceImage": "images/C177/target_top_face.png"}, "__sample_id__": "C177"} +{"taskType": "roll_to_target_top_face", "code": "C178", "name": "Goal Roll C178", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "P", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "arrow_down", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "J", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "5", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "P", "rotation": 90}, "FRONT": {"patternId": "arrow_down", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "J", "rotation": 180}, "BOTTOM": {"patternId": "5", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "5", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C178/initial_net.png", "targetTopFaceImage": "../images/C178/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 2, "targetRotationOffset": 90, "levelId": 178, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-178.json"}, "rollSequence": ["S", "S", "W", "W"], "observedPathFaces": [{"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "P", "rotation": 90}, "FRONT": {"patternId": "arrow_down", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "J", "rotation": 180}, "BOTTOM": {"patternId": "5", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C178\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=5, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=J, rotation=180] [TOP: patternId=P, rotation=90] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=arrow_down, rotation=180]\n [BOTTOM: patternId=5, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=J, rotation=180\n- TOP: patternId=P, rotation=90\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=arrow_down, rotation=180\n- BOTTOM: patternId=5, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C178/initial_net.png", "targetTopFaceImage": "images/C178/target_top_face.png"}, "__sample_id__": "C178"} +{"taskType": "roll_to_target_top_face", "code": "C179", "name": "Goal Roll C179", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "L", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "N", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "J", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "circle", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "H", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "L", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 270}, "RIGHT": {"patternId": "J", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 90}, "BOTTOM": {"patternId": "H", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "L", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C179/initial_net.png", "targetTopFaceImage": "../images/C179/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 4, "targetRotationOffset": 180, "levelId": 179, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-179.json"}, "rollSequence": ["E", "E", "S", "S", "E"], "observedPathFaces": [{"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "S", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "L", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 270}, "RIGHT": {"patternId": "J", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 90}, "BOTTOM": {"patternId": "H", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C179\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=L, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=circle, rotation=90] [TOP: patternId=L, rotation=0] [RIGHT: patternId=J, rotation=90]\n [FRONT: patternId=N, rotation=270]\n [BOTTOM: patternId=H, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=circle, rotation=90\n- TOP: patternId=L, rotation=0\n- RIGHT: patternId=J, rotation=90\n- FRONT: patternId=N, rotation=270\n- BOTTOM: patternId=H, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C179/initial_net.png", "targetTopFaceImage": "images/C179/target_top_face.png"}, "__sample_id__": "C179"} +{"taskType": "roll_to_target_top_face", "code": "C180", "name": "Goal Roll C180", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "arrow_up", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "7", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "W", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "arrow_up", "rotation": 180}, "FRONT": {"patternId": "7", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "W", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "7", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C180/initial_net.png", "targetTopFaceImage": "../images/C180/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 180, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-180.json"}, "rollSequence": ["W", "S", "W", "N"], "observedPathFaces": [{"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "arrow_up", "rotation": 180}, "FRONT": {"patternId": "7", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "W", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C180\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=7, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=W, rotation=180] [TOP: patternId=arrow_up, rotation=180] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=7, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=W, rotation=180\n- TOP: patternId=arrow_up, rotation=180\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=7, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C180/initial_net.png", "targetTopFaceImage": "images/C180/target_top_face.png"}, "__sample_id__": "C180"} +{"taskType": "roll_to_target_top_face", "code": "C181", "name": "Goal Roll C181", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "J", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Z", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "7", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "diamond", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "J", "rotation": 0}, "RIGHT": {"patternId": "Z", "rotation": 90}, "BACK": {"patternId": "7", "rotation": 0}, "LEFT": {"patternId": "diamond", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "7", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C181/initial_net.png", "targetTopFaceImage": "../images/C181/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 181, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-181.json"}, "rollSequence": ["S", "E", "W", "W", "W"], "observedPathFaces": [{"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "W", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "J", "rotation": 0}, "RIGHT": {"patternId": "Z", "rotation": 90}, "BACK": {"patternId": "7", "rotation": 0}, "LEFT": {"patternId": "diamond", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C181\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=7, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=7, rotation=0]\n[LEFT: patternId=diamond, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=Z, rotation=90]\n [FRONT: patternId=J, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=7, rotation=0\n- LEFT: patternId=diamond, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=Z, rotation=90\n- FRONT: patternId=J, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C181/initial_net.png", "targetTopFaceImage": "images/C181/target_top_face.png"}, "__sample_id__": "C181"} +{"taskType": "roll_to_target_top_face", "code": "C182", "name": "Goal Roll C182", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "1", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "4", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "V", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "1", "rotation": 180}, "RIGHT": {"patternId": "4", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "V", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "4", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C182/initial_net.png", "targetTopFaceImage": "../images/C182/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 182, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-182.json"}, "rollSequence": ["W", "S", "S", "N"], "observedPathFaces": [{"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "S", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "1", "rotation": 180}, "RIGHT": {"patternId": "4", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "V", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C182\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=4, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=V, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=4, rotation=90]\n [FRONT: patternId=1, rotation=180]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=V, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=4, rotation=90\n- FRONT: patternId=1, rotation=180\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C182/initial_net.png", "targetTopFaceImage": "images/C182/target_top_face.png"}, "__sample_id__": "C182"} +{"taskType": "roll_to_target_top_face", "code": "C183", "name": "Goal Roll C183", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "G", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "smile", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "D", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "8", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "G", "rotation": 180}, "RIGHT": {"patternId": "smile", "rotation": 270}, "BACK": {"patternId": "D", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "G", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C183/initial_net.png", "targetTopFaceImage": "../images/C183/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 4, "targetRotationOffset": 180, "levelId": 183, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-183.json"}, "rollSequence": ["E", "S", "W", "W", "E"], "observedPathFaces": [{"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "W", "W", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "G", "rotation": 180}, "RIGHT": {"patternId": "smile", "rotation": 270}, "BACK": {"patternId": "D", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C183\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=G, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=D, rotation=90]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=smile, rotation=270]\n [FRONT: patternId=G, rotation=180]\n [BOTTOM: patternId=8, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=D, rotation=90\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=smile, rotation=270\n- FRONT: patternId=G, rotation=180\n- BOTTOM: patternId=8, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C183/initial_net.png", "targetTopFaceImage": "images/C183/target_top_face.png"}, "__sample_id__": "C183"} +{"taskType": "roll_to_target_top_face", "code": "C184", "name": "Goal Roll C184", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "T", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "H", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "D", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "W", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "T", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "H", "rotation": 0}, "BACK": {"patternId": "D", "rotation": 180}, "LEFT": {"patternId": "W", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "H", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C184/initial_net.png", "targetTopFaceImage": "../images/C184/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 4, "targetRotationOffset": 90, "levelId": 184, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-184.json"}, "rollSequence": ["E", "N", "E", "N"], "observedPathFaces": [{"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "T", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "H", "rotation": 0}, "BACK": {"patternId": "D", "rotation": 180}, "LEFT": {"patternId": "W", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C184\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=H, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=D, rotation=180]\n[LEFT: patternId=W, rotation=270] [TOP: patternId=T, rotation=0] [RIGHT: patternId=H, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=D, rotation=180\n- LEFT: patternId=W, rotation=270\n- TOP: patternId=T, rotation=0\n- RIGHT: patternId=H, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C184/initial_net.png", "targetTopFaceImage": "images/C184/target_top_face.png"}, "__sample_id__": "C184"} +{"taskType": "roll_to_target_top_face", "code": "C185", "name": "Goal Roll C185", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "3", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "8", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "C", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "3", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "8", "rotation": 180}, "LEFT": {"patternId": "C", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "8", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C185/initial_net.png", "targetTopFaceImage": "../images/C185/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 3, "targetRotationOffset": 270, "levelId": 185, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-185.json"}, "rollSequence": ["N", "W", "W", "E"], "observedPathFaces": [{"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "W", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "3", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "8", "rotation": 180}, "LEFT": {"patternId": "C", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C185\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=8, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=8, rotation=180]\n[LEFT: patternId=C, rotation=90] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=3, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=8, rotation=180\n- LEFT: patternId=C, rotation=90\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=3, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C185/initial_net.png", "targetTopFaceImage": "images/C185/target_top_face.png"}, "__sample_id__": "C185"} +{"taskType": "roll_to_target_top_face", "code": "C186", "name": "Goal Roll C186", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "G", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "N", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_down", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_left", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "G", "rotation": 90}, "FRONT": {"patternId": "N", "rotation": 0}, "RIGHT": {"patternId": "arrow_down", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_left", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "arrow_left", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C186/initial_net.png", "targetTopFaceImage": "../images/C186/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 3, "targetRotationOffset": 180, "levelId": 186, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-186.json"}, "rollSequence": ["W", "S", "S", "W", "W"], "observedPathFaces": [{"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "S", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "G", "rotation": 90}, "FRONT": {"patternId": "N", "rotation": 0}, "RIGHT": {"patternId": "arrow_down", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_left", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C186\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=arrow_left, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=arrow_left, rotation=90] [TOP: patternId=G, rotation=90] [RIGHT: patternId=arrow_down, rotation=0]\n [FRONT: patternId=N, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=arrow_left, rotation=90\n- TOP: patternId=G, rotation=90\n- RIGHT: patternId=arrow_down, rotation=0\n- FRONT: patternId=N, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C186/initial_net.png", "targetTopFaceImage": "images/C186/target_top_face.png"}, "__sample_id__": "C186"} +{"taskType": "roll_to_target_top_face", "code": "C187", "name": "Goal Roll C187", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "1", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "4", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "O", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "U", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "1", "rotation": 270}, "FRONT": {"patternId": "4", "rotation": 180}, "RIGHT": {"patternId": "O", "rotation": 0}, "BACK": {"patternId": "U", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "4", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C187/initial_net.png", "targetTopFaceImage": "../images/C187/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 4, "targetRotationOffset": 90, "levelId": 187, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-187.json"}, "rollSequence": ["E", "S", "E", "E", "N"], "observedPathFaces": [{"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "E", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "1", "rotation": 270}, "FRONT": {"patternId": "4", "rotation": 180}, "RIGHT": {"patternId": "O", "rotation": 0}, "BACK": {"patternId": "U", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C187\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=4, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=U, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=1, rotation=270] [RIGHT: patternId=O, rotation=0]\n [FRONT: patternId=4, rotation=180]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=U, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=1, rotation=270\n- RIGHT: patternId=O, rotation=0\n- FRONT: patternId=4, rotation=180\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C187/initial_net.png", "targetTopFaceImage": "images/C187/target_top_face.png"}, "__sample_id__": "C187"} +{"taskType": "roll_to_target_top_face", "code": "C188", "name": "Goal Roll C188", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "J", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "heart", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "E", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "1", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "J", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "heart", "rotation": 0}, "LEFT": {"patternId": "E", "rotation": 270}, "BOTTOM": {"patternId": "1", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "J", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C188/initial_net.png", "targetTopFaceImage": "../images/C188/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 2, "targetRotationOffset": 90, "levelId": 188, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-188.json"}, "rollSequence": ["W", "N", "E", "S", "E"], "observedPathFaces": [{"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "E", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "J", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "heart", "rotation": 0}, "LEFT": {"patternId": "E", "rotation": 270}, "BOTTOM": {"patternId": "1", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C188\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=J, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=heart, rotation=0]\n[LEFT: patternId=E, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=J, rotation=270]\n [BOTTOM: patternId=1, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=heart, rotation=0\n- LEFT: patternId=E, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=J, rotation=270\n- BOTTOM: patternId=1, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C188/initial_net.png", "targetTopFaceImage": "images/C188/target_top_face.png"}, "__sample_id__": "C188"} +{"taskType": "roll_to_target_top_face", "code": "C189", "name": "Goal Roll C189", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "8", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "heart", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "C", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "8", "rotation": 180}, "RIGHT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "C", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "8", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C189/initial_net.png", "targetTopFaceImage": "../images/C189/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 189, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-189.json"}, "rollSequence": ["S", "N", "E", "S"], "observedPathFaces": [{"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "N", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "8", "rotation": 180}, "RIGHT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "C", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C189\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=8, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=heart, rotation=270]\n [FRONT: patternId=8, rotation=180]\n [BOTTOM: patternId=C, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=heart, rotation=270\n- FRONT: patternId=8, rotation=180\n- BOTTOM: patternId=C, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C189/initial_net.png", "targetTopFaceImage": "images/C189/target_top_face.png"}, "__sample_id__": "C189"} +{"taskType": "roll_to_target_top_face", "code": "C190", "name": "Goal Roll C190", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "7", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "arrow_down", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "Q", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "7", "rotation": 180}, "FRONT": {"patternId": "arrow_down", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "Q", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "Q", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C190/initial_net.png", "targetTopFaceImage": "../images/C190/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 3, "targetRotationOffset": 90, "levelId": 190, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-190.json"}, "rollSequence": ["N", "N", "N", "S"], "observedPathFaces": [{"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "N", "S"]}, "legacy_answer": {"TOP": {"patternId": "7", "rotation": 180}, "FRONT": {"patternId": "arrow_down", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "Q", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C190\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=Q, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=Q, rotation=90]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=7, rotation=180] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=arrow_down, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Q, rotation=90\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=7, rotation=180\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=arrow_down, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C190/initial_net.png", "targetTopFaceImage": "images/C190/target_top_face.png"}, "__sample_id__": "C190"} +{"taskType": "roll_to_target_top_face", "code": "C191", "name": "Goal Roll C191", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "arrow_left", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "smile", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "I", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "M", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "arrow_left", "rotation": 90}, "FRONT": {"patternId": "smile", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 180}, "LEFT": {"patternId": "M", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "I", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C191/initial_net.png", "targetTopFaceImage": "../images/C191/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 191, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-191.json"}, "rollSequence": ["S", "W", "S", "W"], "observedPathFaces": [{"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "arrow_left", "rotation": 90}, "FRONT": {"patternId": "smile", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 180}, "LEFT": {"patternId": "M", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C191\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=I, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=I, rotation=180]\n[LEFT: patternId=M, rotation=180] [TOP: patternId=arrow_left, rotation=90] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=smile, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=I, rotation=180\n- LEFT: patternId=M, rotation=180\n- TOP: patternId=arrow_left, rotation=90\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=smile, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C191/initial_net.png", "targetTopFaceImage": "images/C191/target_top_face.png"}, "__sample_id__": "C191"} +{"taskType": "roll_to_target_top_face", "code": "C192", "name": "Goal Roll C192", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "8", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "P", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "star", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "8", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_right", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "8", "rotation": 270}, "FRONT": {"patternId": "P", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 180}, "LEFT": {"patternId": "8", "rotation": 90}, "BOTTOM": {"patternId": "arrow_right", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "star", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C192/initial_net.png", "targetTopFaceImage": "../images/C192/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 5, "targetRotationOffset": 90, "levelId": 192, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-192.json"}, "rollSequence": ["W", "W", "N", "N", "N"], "observedPathFaces": [{"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "N", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "8", "rotation": 270}, "FRONT": {"patternId": "P", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 180}, "LEFT": {"patternId": "8", "rotation": 90}, "BOTTOM": {"patternId": "arrow_right", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C192\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=star, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=star, rotation=180]\n[LEFT: patternId=8, rotation=90] [TOP: patternId=8, rotation=270] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=P, rotation=90]\n [BOTTOM: patternId=arrow_right, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=star, rotation=180\n- LEFT: patternId=8, rotation=90\n- TOP: patternId=8, rotation=270\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=P, rotation=90\n- BOTTOM: patternId=arrow_right, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C192/initial_net.png", "targetTopFaceImage": "images/C192/target_top_face.png"}, "__sample_id__": "C192"} +{"taskType": "roll_to_target_top_face", "code": "C193", "name": "Goal Roll C193", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "5", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "I", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_right", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "I", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "5", "rotation": 90}, "RIGHT": {"patternId": "I", "rotation": 90}, "BACK": {"patternId": "arrow_right", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "I", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "5", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C193/initial_net.png", "targetTopFaceImage": "../images/C193/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 193, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-193.json"}, "rollSequence": ["N", "E", "S", "E", "N"], "observedPathFaces": [{"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "S", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "5", "rotation": 90}, "RIGHT": {"patternId": "I", "rotation": 90}, "BACK": {"patternId": "arrow_right", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "I", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C193\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=5, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_right, rotation=90]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=I, rotation=90]\n [FRONT: patternId=5, rotation=90]\n [BOTTOM: patternId=I, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_right, rotation=90\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=I, rotation=90\n- FRONT: patternId=5, rotation=90\n- BOTTOM: patternId=I, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C193/initial_net.png", "targetTopFaceImage": "images/C193/target_top_face.png"}, "__sample_id__": "C193"} +{"taskType": "roll_to_target_top_face", "code": "C194", "name": "Goal Roll C194", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "G", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_up", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_right", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "R", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "G", "rotation": 90}, "BACK": {"patternId": "arrow_up", "rotation": 180}, "LEFT": {"patternId": "arrow_right", "rotation": 90}, "BOTTOM": {"patternId": "R", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "G", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C194/initial_net.png", "targetTopFaceImage": "../images/C194/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 194, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-194.json"}, "rollSequence": ["W", "N", "N", "E"], "observedPathFaces": [{"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "G", "rotation": 90}, "BACK": {"patternId": "arrow_up", "rotation": 180}, "LEFT": {"patternId": "arrow_right", "rotation": 90}, "BOTTOM": {"patternId": "R", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C194\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=G, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_up, rotation=180]\n[LEFT: patternId=arrow_right, rotation=90] [TOP: patternId=?, rotation=0] [RIGHT: patternId=G, rotation=90]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=R, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_up, rotation=180\n- LEFT: patternId=arrow_right, rotation=90\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=G, rotation=90\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=R, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C194/initial_net.png", "targetTopFaceImage": "images/C194/target_top_face.png"}, "__sample_id__": "C194"} +{"taskType": "roll_to_target_top_face", "code": "C195", "name": "Goal Roll C195", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "W", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "plus", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "G", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "W", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "plus", "rotation": 270}, "BACK": {"patternId": "G", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "G", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C195/initial_net.png", "targetTopFaceImage": "../images/C195/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 195, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-195.json"}, "rollSequence": ["N", "N", "E", "S"], "observedPathFaces": [{"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "W", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "plus", "rotation": 270}, "BACK": {"patternId": "G", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C195\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=G, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=G, rotation=270]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=W, rotation=0] [RIGHT: patternId=plus, rotation=270]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=G, rotation=270\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=W, rotation=0\n- RIGHT: patternId=plus, rotation=270\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C195/initial_net.png", "targetTopFaceImage": "images/C195/target_top_face.png"}, "__sample_id__": "C195"} +{"taskType": "roll_to_target_top_face", "code": "C196", "name": "Goal Roll C196", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "D", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "Q", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "X", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "Q", "rotation": 90}, "LEFT": {"patternId": "X", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "D", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C196/initial_net.png", "targetTopFaceImage": "../images/C196/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 2, "targetRotationOffset": 90, "levelId": 196, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-196.json"}, "rollSequence": ["W", "N", "S", "S"], "observedPathFaces": [{"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "Q", "rotation": 90}, "LEFT": {"patternId": "X", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C196\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=D, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=Q, rotation=90]\n[LEFT: patternId=X, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=D, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Q, rotation=90\n- LEFT: patternId=X, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=D, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C196/initial_net.png", "targetTopFaceImage": "images/C196/target_top_face.png"}, "__sample_id__": "C196"} +{"taskType": "roll_to_target_top_face", "code": "C197", "name": "Goal Roll C197", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "T", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "7", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "5", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "3", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "T", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "7", "rotation": 90}, "BACK": {"patternId": "5", "rotation": 270}, "LEFT": {"patternId": "3", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "7", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C197/initial_net.png", "targetTopFaceImage": "../images/C197/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 4, "targetRotationOffset": 270, "levelId": 197, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-197.json"}, "rollSequence": ["N", "E", "N", "N"], "observedPathFaces": [{"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "T", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "7", "rotation": 90}, "BACK": {"patternId": "5", "rotation": 270}, "LEFT": {"patternId": "3", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C197\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=7, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=5, rotation=270]\n[LEFT: patternId=3, rotation=90] [TOP: patternId=T, rotation=90] [RIGHT: patternId=7, rotation=90]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=5, rotation=270\n- LEFT: patternId=3, rotation=90\n- TOP: patternId=T, rotation=90\n- RIGHT: patternId=7, rotation=90\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C197/initial_net.png", "targetTopFaceImage": "images/C197/target_top_face.png"}, "__sample_id__": "C197"} +{"taskType": "roll_to_target_top_face", "code": "C198", "name": "Goal Roll C198", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "square", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "arrow_right", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "F", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "Z", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "square", "rotation": 270}, "FRONT": {"patternId": "arrow_right", "rotation": 180}, "RIGHT": {"patternId": "F", "rotation": 90}, "BACK": {"patternId": "Z", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "arrow_right", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C198/initial_net.png", "targetTopFaceImage": "../images/C198/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 2, "targetRotationOffset": 90, "levelId": 198, "moveCount": 5, "sourceLevelPath": "levels/reconstruct/generated-198.json"}, "rollSequence": ["E", "N", "S", "E", "S"], "observedPathFaces": [{"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "S", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "square", "rotation": 270}, "FRONT": {"patternId": "arrow_right", "rotation": 180}, "RIGHT": {"patternId": "F", "rotation": 90}, "BACK": {"patternId": "Z", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C198\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=arrow_right, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=Z, rotation=270]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=square, rotation=270] [RIGHT: patternId=F, rotation=90]\n [FRONT: patternId=arrow_right, rotation=180]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Z, rotation=270\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=square, rotation=270\n- RIGHT: patternId=F, rotation=90\n- FRONT: patternId=arrow_right, rotation=180\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C198/initial_net.png", "targetTopFaceImage": "images/C198/target_top_face.png"}, "__sample_id__": "C198"} +{"taskType": "roll_to_target_top_face", "code": "C199", "name": "Goal Roll C199", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "circle", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "heart", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "B", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "M", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "circle", "rotation": 180}, "RIGHT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "B", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "M", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "circle", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C199/initial_net.png", "targetTopFaceImage": "../images/C199/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 4, "targetRotationOffset": 270, "levelId": 199, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-199.json"}, "rollSequence": ["E", "S", "W", "W"], "observedPathFaces": [{"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "circle", "rotation": 180}, "RIGHT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "B", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "M", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C199\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=circle, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=B, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=heart, rotation=270]\n [FRONT: patternId=circle, rotation=180]\n [BOTTOM: patternId=M, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=B, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=heart, rotation=270\n- FRONT: patternId=circle, rotation=180\n- BOTTOM: patternId=M, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C199/initial_net.png", "targetTopFaceImage": "images/C199/target_top_face.png"}, "__sample_id__": "C199"} +{"taskType": "roll_to_target_top_face", "code": "C200", "name": "Goal Roll C200", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "U", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "L", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "E", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "Y", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "U", "rotation": 0}, "FRONT": {"patternId": "L", "rotation": 270}, "RIGHT": {"patternId": "E", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "E", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C200/initial_net.png", "targetTopFaceImage": "../images/C200/target_top_face.png"}, "metadata": {"difficulty": 2, "tier": 2, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 200, "moveCount": 4, "sourceLevelPath": "levels/reconstruct/generated-200.json"}, "rollSequence": ["W", "W", "S", "W"], "observedPathFaces": [{"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "U", "rotation": 0}, "FRONT": {"patternId": "L", "rotation": 270}, "RIGHT": {"patternId": "E", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C200\n- task_type: roll_to_target_top_face\n- difficulty: 2\n- target_top_face: patternId=E, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=Y, rotation=270] [TOP: patternId=U, rotation=0] [RIGHT: patternId=E, rotation=0]\n [FRONT: patternId=L, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=Y, rotation=270\n- TOP: patternId=U, rotation=0\n- RIGHT: patternId=E, rotation=0\n- FRONT: patternId=L, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C200/initial_net.png", "targetTopFaceImage": "images/C200/target_top_face.png"}, "__sample_id__": "C200"} +{"taskType": "roll_to_target_top_face", "code": "C201", "name": "Goal Roll C201", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "heart", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_up", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "N", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "1", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_up", "rotation": 270}, "LEFT": {"patternId": "N", "rotation": 0}, "BOTTOM": {"patternId": "1", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "heart", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C201/initial_net.png", "targetTopFaceImage": "../images/C201/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 6, "targetRotationOffset": 90, "levelId": 201, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-201.json"}, "rollSequence": ["N", "W", "S", "W", "N", "N", "E"], "observedPathFaces": [{"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "S", "W", "N", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_up", "rotation": 270}, "LEFT": {"patternId": "N", "rotation": 0}, "BOTTOM": {"patternId": "1", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C201\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=heart, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_up, rotation=270]\n[LEFT: patternId=N, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=heart, rotation=180]\n [BOTTOM: patternId=1, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_up, rotation=270\n- LEFT: patternId=N, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=heart, rotation=180\n- BOTTOM: patternId=1, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C201/initial_net.png", "targetTopFaceImage": "images/C201/target_top_face.png"}, "__sample_id__": "C201"} +{"taskType": "roll_to_target_top_face", "code": "C202", "name": "Goal Roll C202", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "6", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "7", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_down", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "N", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "X", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "6", "rotation": 180}, "RIGHT": {"patternId": "7", "rotation": 90}, "BACK": {"patternId": "arrow_down", "rotation": 180}, "LEFT": {"patternId": "N", "rotation": 90}, "BOTTOM": {"patternId": "X", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "N", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C202/initial_net.png", "targetTopFaceImage": "../images/C202/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 5, "targetRotationOffset": 270, "levelId": 202, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-202.json"}, "rollSequence": ["N", "W", "S", "W", "S", "E"], "observedPathFaces": [{"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "S", "W", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "6", "rotation": 180}, "RIGHT": {"patternId": "7", "rotation": 90}, "BACK": {"patternId": "arrow_down", "rotation": 180}, "LEFT": {"patternId": "N", "rotation": 90}, "BOTTOM": {"patternId": "X", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C202\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=N, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_down, rotation=180]\n[LEFT: patternId=N, rotation=90] [TOP: patternId=?, rotation=0] [RIGHT: patternId=7, rotation=90]\n [FRONT: patternId=6, rotation=180]\n [BOTTOM: patternId=X, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_down, rotation=180\n- LEFT: patternId=N, rotation=90\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=7, rotation=90\n- FRONT: patternId=6, rotation=180\n- BOTTOM: patternId=X, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C202/initial_net.png", "targetTopFaceImage": "images/C202/target_top_face.png"}, "__sample_id__": "C202"} +{"taskType": "roll_to_target_top_face", "code": "C203", "name": "Goal Roll C203", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "2", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "circle", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "J", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "Q", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "2", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 0}, "LEFT": {"patternId": "J", "rotation": 90}, "BOTTOM": {"patternId": "Q", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "Q", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C203/initial_net.png", "targetTopFaceImage": "../images/C203/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 5, "targetRotationOffset": 270, "levelId": 203, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-203.json"}, "rollSequence": ["W", "E", "W", "N", "W", "S"], "observedPathFaces": [{"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "E", "W", "N", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "2", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 0}, "LEFT": {"patternId": "J", "rotation": 90}, "BOTTOM": {"patternId": "Q", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C203\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=Q, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=circle, rotation=0]\n[LEFT: patternId=J, rotation=90] [TOP: patternId=2, rotation=180] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=Q, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=circle, rotation=0\n- LEFT: patternId=J, rotation=90\n- TOP: patternId=2, rotation=180\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=Q, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C203/initial_net.png", "targetTopFaceImage": "images/C203/target_top_face.png"}, "__sample_id__": "C203"} +{"taskType": "roll_to_target_top_face", "code": "C204", "name": "Goal Roll C204", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "8", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "E", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "R", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "2", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "N", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "8", "rotation": 0}, "FRONT": {"patternId": "E", "rotation": 180}, "RIGHT": {"patternId": "R", "rotation": 270}, "BACK": {"patternId": "2", "rotation": 270}, "LEFT": {"patternId": "N", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "R", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C204/initial_net.png", "targetTopFaceImage": "../images/C204/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 6, "targetRotationOffset": 90, "levelId": 204, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-204.json"}, "rollSequence": ["E", "S", "S", "E", "S", "W", "W"], "observedPathFaces": [{"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "S", "E", "S", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "8", "rotation": 0}, "FRONT": {"patternId": "E", "rotation": 180}, "RIGHT": {"patternId": "R", "rotation": 270}, "BACK": {"patternId": "2", "rotation": 270}, "LEFT": {"patternId": "N", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C204\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=R, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=2, rotation=270]\n[LEFT: patternId=N, rotation=270] [TOP: patternId=8, rotation=0] [RIGHT: patternId=R, rotation=270]\n [FRONT: patternId=E, rotation=180]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=2, rotation=270\n- LEFT: patternId=N, rotation=270\n- TOP: patternId=8, rotation=0\n- RIGHT: patternId=R, rotation=270\n- FRONT: patternId=E, rotation=180\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C204/initial_net.png", "targetTopFaceImage": "images/C204/target_top_face.png"}, "__sample_id__": "C204"} +{"taskType": "roll_to_target_top_face", "code": "C205", "name": "Goal Roll C205", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "I", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "3", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "1", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "diamond", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "I", "rotation": 0}, "FRONT": {"patternId": "3", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "1", "rotation": 90}, "BOTTOM": {"patternId": "diamond", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "I", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C205/initial_net.png", "targetTopFaceImage": "../images/C205/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 6, "targetRotationOffset": 270, "levelId": 205, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-205.json"}, "rollSequence": ["W", "S", "W", "N", "E", "N"], "observedPathFaces": [{"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "W", "N", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "I", "rotation": 0}, "FRONT": {"patternId": "3", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "1", "rotation": 90}, "BOTTOM": {"patternId": "diamond", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C205\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=I, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=1, rotation=90] [TOP: patternId=I, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=3, rotation=0]\n [BOTTOM: patternId=diamond, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=1, rotation=90\n- TOP: patternId=I, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=3, rotation=0\n- BOTTOM: patternId=diamond, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C205/initial_net.png", "targetTopFaceImage": "images/C205/target_top_face.png"}, "__sample_id__": "C205"} +{"taskType": "roll_to_target_top_face", "code": "C206", "name": "Goal Roll C206", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "Y", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_left", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "P", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_right", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "Y", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 180}, "LEFT": {"patternId": "P", "rotation": 90}, "BOTTOM": {"patternId": "arrow_right", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "arrow_right", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C206/initial_net.png", "targetTopFaceImage": "../images/C206/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 5, "targetRotationOffset": 90, "levelId": 206, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-206.json"}, "rollSequence": ["W", "E", "N", "W", "N", "E", "S"], "observedPathFaces": [{"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "E", "N", "W", "N", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "Y", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 180}, "LEFT": {"patternId": "P", "rotation": 90}, "BOTTOM": {"patternId": "arrow_right", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C206\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=arrow_right, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_left, rotation=180]\n[LEFT: patternId=P, rotation=90] [TOP: patternId=Y, rotation=180] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=arrow_right, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_left, rotation=180\n- LEFT: patternId=P, rotation=90\n- TOP: patternId=Y, rotation=180\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=arrow_right, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C206/initial_net.png", "targetTopFaceImage": "images/C206/target_top_face.png"}, "__sample_id__": "C206"} +{"taskType": "roll_to_target_top_face", "code": "C207", "name": "Goal Roll C207", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "M", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "J", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Z", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "E", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "D", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_down", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "M", "rotation": 90}, "FRONT": {"patternId": "J", "rotation": 0}, "RIGHT": {"patternId": "Z", "rotation": 90}, "BACK": {"patternId": "E", "rotation": 0}, "LEFT": {"patternId": "D", "rotation": 90}, "BOTTOM": {"patternId": "arrow_down", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "arrow_down", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C207/initial_net.png", "targetTopFaceImage": "../images/C207/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 3, "targetRotationOffset": 180, "levelId": 207, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-207.json"}, "rollSequence": ["N", "W", "N", "N", "W", "N"], "observedPathFaces": [{"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "N", "N", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "M", "rotation": 90}, "FRONT": {"patternId": "J", "rotation": 0}, "RIGHT": {"patternId": "Z", "rotation": 90}, "BACK": {"patternId": "E", "rotation": 0}, "LEFT": {"patternId": "D", "rotation": 90}, "BOTTOM": {"patternId": "arrow_down", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C207\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=arrow_down, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=E, rotation=0]\n[LEFT: patternId=D, rotation=90] [TOP: patternId=M, rotation=90] [RIGHT: patternId=Z, rotation=90]\n [FRONT: patternId=J, rotation=0]\n [BOTTOM: patternId=arrow_down, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=E, rotation=0\n- LEFT: patternId=D, rotation=90\n- TOP: patternId=M, rotation=90\n- RIGHT: patternId=Z, rotation=90\n- FRONT: patternId=J, rotation=0\n- BOTTOM: patternId=arrow_down, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C207/initial_net.png", "targetTopFaceImage": "images/C207/target_top_face.png"}, "__sample_id__": "C207"} +{"taskType": "roll_to_target_top_face", "code": "C208", "name": "Goal Roll C208", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "O", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "circle", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "circle", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "Y", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "F", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "O", "rotation": 0}, "FRONT": {"patternId": "circle", "rotation": 90}, "RIGHT": {"patternId": "circle", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 180}, "BOTTOM": {"patternId": "F", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "F", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C208/initial_net.png", "targetTopFaceImage": "../images/C208/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 2, "targetRotationOffset": 270, "levelId": 208, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-208.json"}, "rollSequence": ["S", "S", "E", "E", "N", "E"], "observedPathFaces": [{"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "E", "E", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 0}, "FRONT": {"patternId": "circle", "rotation": 90}, "RIGHT": {"patternId": "circle", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 180}, "BOTTOM": {"patternId": "F", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C208\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=F, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=Y, rotation=180] [TOP: patternId=O, rotation=0] [RIGHT: patternId=circle, rotation=180]\n [FRONT: patternId=circle, rotation=90]\n [BOTTOM: patternId=F, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=Y, rotation=180\n- TOP: patternId=O, rotation=0\n- RIGHT: patternId=circle, rotation=180\n- FRONT: patternId=circle, rotation=90\n- BOTTOM: patternId=F, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C208/initial_net.png", "targetTopFaceImage": "images/C208/target_top_face.png"}, "__sample_id__": "C208"} +{"taskType": "roll_to_target_top_face", "code": "C209", "name": "Goal Roll C209", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "K", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "2", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "3", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "B", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "O", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "K", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 180}, "RIGHT": {"patternId": "3", "rotation": 180}, "BACK": {"patternId": "B", "rotation": 0}, "LEFT": {"patternId": "O", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "B", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C209/initial_net.png", "targetTopFaceImage": "../images/C209/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 5, "targetRotationOffset": 90, "levelId": 209, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-209.json"}, "rollSequence": ["W", "S", "W", "S", "E", "N", "N"], "observedPathFaces": [{"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "W", "S", "E", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "K", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 180}, "RIGHT": {"patternId": "3", "rotation": 180}, "BACK": {"patternId": "B", "rotation": 0}, "LEFT": {"patternId": "O", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C209\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=B, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=B, rotation=0]\n[LEFT: patternId=O, rotation=270] [TOP: patternId=K, rotation=0] [RIGHT: patternId=3, rotation=180]\n [FRONT: patternId=2, rotation=180]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=B, rotation=0\n- LEFT: patternId=O, rotation=270\n- TOP: patternId=K, rotation=0\n- RIGHT: patternId=3, rotation=180\n- FRONT: patternId=2, rotation=180\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C209/initial_net.png", "targetTopFaceImage": "images/C209/target_top_face.png"}, "__sample_id__": "C209"} +{"taskType": "roll_to_target_top_face", "code": "C210", "name": "Goal Roll C210", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "N", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "triangle", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_up", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "3", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "N", "rotation": 270}, "BACK": {"patternId": "triangle", "rotation": 0}, "LEFT": {"patternId": "arrow_up", "rotation": 270}, "BOTTOM": {"patternId": "3", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "arrow_up", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C210/initial_net.png", "targetTopFaceImage": "../images/C210/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 3, "targetRotationOffset": 180, "levelId": 210, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-210.json"}, "rollSequence": ["W", "E", "E", "N", "N", "W"], "observedPathFaces": [{"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "E", "E", "N", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "N", "rotation": 270}, "BACK": {"patternId": "triangle", "rotation": 0}, "LEFT": {"patternId": "arrow_up", "rotation": 270}, "BOTTOM": {"patternId": "3", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C210\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=arrow_up, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=triangle, rotation=0]\n[LEFT: patternId=arrow_up, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=N, rotation=270]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=3, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=triangle, rotation=0\n- LEFT: patternId=arrow_up, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=N, rotation=270\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=3, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C210/initial_net.png", "targetTopFaceImage": "images/C210/target_top_face.png"}, "__sample_id__": "C210"} +{"taskType": "roll_to_target_top_face", "code": "C211", "name": "Goal Roll C211", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "8", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "U", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "1", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "U", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "6", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "8", "rotation": 0}, "RIGHT": {"patternId": "U", "rotation": 0}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "U", "rotation": 270}, "BOTTOM": {"patternId": "6", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "1", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C211/initial_net.png", "targetTopFaceImage": "../images/C211/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 211, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-211.json"}, "rollSequence": ["S", "W", "W", "W", "N", "S"], "observedPathFaces": [{"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "W", "W", "N", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "8", "rotation": 0}, "RIGHT": {"patternId": "U", "rotation": 0}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "U", "rotation": 270}, "BOTTOM": {"patternId": "6", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C211\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=1, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=1, rotation=180]\n[LEFT: patternId=U, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=U, rotation=0]\n [FRONT: patternId=8, rotation=0]\n [BOTTOM: patternId=6, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=1, rotation=180\n- LEFT: patternId=U, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=U, rotation=0\n- FRONT: patternId=8, rotation=0\n- BOTTOM: patternId=6, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C211/initial_net.png", "targetTopFaceImage": "images/C211/target_top_face.png"}, "__sample_id__": "C211"} +{"taskType": "roll_to_target_top_face", "code": "C212", "name": "Goal Roll C212", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "7", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "W", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "I", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "circle", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "6", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "7", "rotation": 90}, "FRONT": {"patternId": "W", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "6", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C212/initial_net.png", "targetTopFaceImage": "../images/C212/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 2, "targetRotationOffset": 90, "levelId": 212, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-212.json"}, "rollSequence": ["S", "S", "N", "W", "N", "W"], "observedPathFaces": [{"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "N", "W", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "7", "rotation": 90}, "FRONT": {"patternId": "W", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C212\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=6, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=I, rotation=0]\n[LEFT: patternId=circle, rotation=0] [TOP: patternId=7, rotation=90] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=W, rotation=90]\n [BOTTOM: patternId=6, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=I, rotation=0\n- LEFT: patternId=circle, rotation=0\n- TOP: patternId=7, rotation=90\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=W, rotation=90\n- BOTTOM: patternId=6, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C212/initial_net.png", "targetTopFaceImage": "images/C212/target_top_face.png"}, "__sample_id__": "C212"} +{"taskType": "roll_to_target_top_face", "code": "C213", "name": "Goal Roll C213", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "Y", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "plus", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "D", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "V", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "B", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "B", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "Y", "rotation": 90}, "FRONT": {"patternId": "plus", "rotation": 180}, "RIGHT": {"patternId": "D", "rotation": 180}, "BACK": {"patternId": "V", "rotation": 270}, "LEFT": {"patternId": "B", "rotation": 0}, "BOTTOM": {"patternId": "B", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "V", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C213/initial_net.png", "targetTopFaceImage": "../images/C213/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 3, "targetRotationOffset": 270, "levelId": 213, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-213.json"}, "rollSequence": ["N", "S", "S", "E", "S", "W", "S"], "observedPathFaces": [{"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "S", "S", "E", "S", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "Y", "rotation": 90}, "FRONT": {"patternId": "plus", "rotation": 180}, "RIGHT": {"patternId": "D", "rotation": 180}, "BACK": {"patternId": "V", "rotation": 270}, "LEFT": {"patternId": "B", "rotation": 0}, "BOTTOM": {"patternId": "B", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C213\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=V, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=V, rotation=270]\n[LEFT: patternId=B, rotation=0] [TOP: patternId=Y, rotation=90] [RIGHT: patternId=D, rotation=180]\n [FRONT: patternId=plus, rotation=180]\n [BOTTOM: patternId=B, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=V, rotation=270\n- LEFT: patternId=B, rotation=0\n- TOP: patternId=Y, rotation=90\n- RIGHT: patternId=D, rotation=180\n- FRONT: patternId=plus, rotation=180\n- BOTTOM: patternId=B, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C213/initial_net.png", "targetTopFaceImage": "images/C213/target_top_face.png"}, "__sample_id__": "C213"} +{"taskType": "roll_to_target_top_face", "code": "C214", "name": "Goal Roll C214", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "arrow_up", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "8", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "D", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "Y", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "arrow_up", "rotation": 180}, "FRONT": {"patternId": "8", "rotation": 90}, "RIGHT": {"patternId": "D", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "Y", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C214/initial_net.png", "targetTopFaceImage": "../images/C214/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 214, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-214.json"}, "rollSequence": ["E", "S", "S", "N", "E", "S"], "observedPathFaces": [{"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "S", "N", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "arrow_up", "rotation": 180}, "FRONT": {"patternId": "8", "rotation": 90}, "RIGHT": {"patternId": "D", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C214\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=Y, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=Y, rotation=270] [TOP: patternId=arrow_up, rotation=180] [RIGHT: patternId=D, rotation=0]\n [FRONT: patternId=8, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=Y, rotation=270\n- TOP: patternId=arrow_up, rotation=180\n- RIGHT: patternId=D, rotation=0\n- FRONT: patternId=8, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C214/initial_net.png", "targetTopFaceImage": "images/C214/target_top_face.png"}, "__sample_id__": "C214"} +{"taskType": "roll_to_target_top_face", "code": "C215", "name": "Goal Roll C215", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "triangle", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "arrow_up", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "L", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "K", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "P", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "circle", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "triangle", "rotation": 270}, "FRONT": {"patternId": "arrow_up", "rotation": 0}, "RIGHT": {"patternId": "L", "rotation": 90}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "P", "rotation": 90}, "BOTTOM": {"patternId": "circle", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "circle", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C215/initial_net.png", "targetTopFaceImage": "../images/C215/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 2, "targetRotationOffset": 180, "levelId": 215, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-215.json"}, "rollSequence": ["S", "S", "W", "S", "W", "S", "E"], "observedPathFaces": [{"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "W", "S", "W", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "triangle", "rotation": 270}, "FRONT": {"patternId": "arrow_up", "rotation": 0}, "RIGHT": {"patternId": "L", "rotation": 90}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "P", "rotation": 90}, "BOTTOM": {"patternId": "circle", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C215\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=circle, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=K, rotation=270]\n[LEFT: patternId=P, rotation=90] [TOP: patternId=triangle, rotation=270] [RIGHT: patternId=L, rotation=90]\n [FRONT: patternId=arrow_up, rotation=0]\n [BOTTOM: patternId=circle, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=K, rotation=270\n- LEFT: patternId=P, rotation=90\n- TOP: patternId=triangle, rotation=270\n- RIGHT: patternId=L, rotation=90\n- FRONT: patternId=arrow_up, rotation=0\n- BOTTOM: patternId=circle, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C215/initial_net.png", "targetTopFaceImage": "images/C215/target_top_face.png"}, "__sample_id__": "C215"} +{"taskType": "roll_to_target_top_face", "code": "C216", "name": "Goal Roll C216", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "S", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "S", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "5", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "circle", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "Z", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "E", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "S", "rotation": 180}, "FRONT": {"patternId": "S", "rotation": 90}, "RIGHT": {"patternId": "5", "rotation": 180}, "BACK": {"patternId": "circle", "rotation": 270}, "LEFT": {"patternId": "Z", "rotation": 0}, "BOTTOM": {"patternId": "E", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "5", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C216/initial_net.png", "targetTopFaceImage": "../images/C216/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 4, "targetRotationOffset": 270, "levelId": 216, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-216.json"}, "rollSequence": ["E", "E", "N", "E", "N", "E"], "observedPathFaces": [{"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "N", "E", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "S", "rotation": 180}, "FRONT": {"patternId": "S", "rotation": 90}, "RIGHT": {"patternId": "5", "rotation": 180}, "BACK": {"patternId": "circle", "rotation": 270}, "LEFT": {"patternId": "Z", "rotation": 0}, "BOTTOM": {"patternId": "E", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C216\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=5, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=circle, rotation=270]\n[LEFT: patternId=Z, rotation=0] [TOP: patternId=S, rotation=180] [RIGHT: patternId=5, rotation=180]\n [FRONT: patternId=S, rotation=90]\n [BOTTOM: patternId=E, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=circle, rotation=270\n- LEFT: patternId=Z, rotation=0\n- TOP: patternId=S, rotation=180\n- RIGHT: patternId=5, rotation=180\n- FRONT: patternId=S, rotation=90\n- BOTTOM: patternId=E, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C216/initial_net.png", "targetTopFaceImage": "images/C216/target_top_face.png"}, "__sample_id__": "C216"} +{"taskType": "roll_to_target_top_face", "code": "C217", "name": "Goal Roll C217", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "square", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "square", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "star", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "I", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 270}, "RIGHT": {"patternId": "square", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "star", "rotation": 270}, "BOTTOM": {"patternId": "I", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 6, "stepNumber": 7, "patternId": "star", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C217/initial_net.png", "targetTopFaceImage": "../images/C217/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 7, "targetRotationOffset": 180, "levelId": 217, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-217.json"}, "rollSequence": ["E", "S", "W", "E", "S", "W", "W"], "observedPathFaces": [{"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "W", "E", "S", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 270}, "RIGHT": {"patternId": "square", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "star", "rotation": 270}, "BOTTOM": {"patternId": "I", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C217\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=star, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=star, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=square, rotation=270]\n [FRONT: patternId=square, rotation=270]\n [BOTTOM: patternId=I, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=star, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=square, rotation=270\n- FRONT: patternId=square, rotation=270\n- BOTTOM: patternId=I, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C217/initial_net.png", "targetTopFaceImage": "images/C217/target_top_face.png"}, "__sample_id__": "C217"} +{"taskType": "roll_to_target_top_face", "code": "C218", "name": "Goal Roll C218", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "K", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "Z", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Z", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "Y", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "G", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "K", "rotation": 270}, "FRONT": {"patternId": "Z", "rotation": 180}, "RIGHT": {"patternId": "Z", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 270}, "BOTTOM": {"patternId": "G", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "Z", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C218/initial_net.png", "targetTopFaceImage": "../images/C218/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 218, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-218.json"}, "rollSequence": ["W", "S", "S", "E", "N", "N"], "observedPathFaces": [{"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "S", "E", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "K", "rotation": 270}, "FRONT": {"patternId": "Z", "rotation": 180}, "RIGHT": {"patternId": "Z", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 270}, "BOTTOM": {"patternId": "G", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C218\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=Z, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=Y, rotation=270] [TOP: patternId=K, rotation=270] [RIGHT: patternId=Z, rotation=0]\n [FRONT: patternId=Z, rotation=180]\n [BOTTOM: patternId=G, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=Y, rotation=270\n- TOP: patternId=K, rotation=270\n- RIGHT: patternId=Z, rotation=0\n- FRONT: patternId=Z, rotation=180\n- BOTTOM: patternId=G, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C218/initial_net.png", "targetTopFaceImage": "images/C218/target_top_face.png"}, "__sample_id__": "C218"} +{"taskType": "roll_to_target_top_face", "code": "C219", "name": "Goal Roll C219", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "7", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "triangle", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "D", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "A", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "7", "rotation": 270}, "FRONT": {"patternId": "triangle", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "D", "rotation": 0}, "BOTTOM": {"patternId": "A", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "A", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C219/initial_net.png", "targetTopFaceImage": "../images/C219/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 6, "targetRotationOffset": 270, "levelId": 219, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-219.json"}, "rollSequence": ["S", "W", "E", "N", "S", "S"], "observedPathFaces": [{"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "E", "N", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "7", "rotation": 270}, "FRONT": {"patternId": "triangle", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "D", "rotation": 0}, "BOTTOM": {"patternId": "A", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C219\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=A, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=D, rotation=0] [TOP: patternId=7, rotation=270] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=triangle, rotation=90]\n [BOTTOM: patternId=A, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=D, rotation=0\n- TOP: patternId=7, rotation=270\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=triangle, rotation=90\n- BOTTOM: patternId=A, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C219/initial_net.png", "targetTopFaceImage": "images/C219/target_top_face.png"}, "__sample_id__": "C219"} +{"taskType": "roll_to_target_top_face", "code": "C220", "name": "Goal Roll C220", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "L", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Z", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "M", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "G", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "L", "rotation": 180}, "RIGHT": {"patternId": "Z", "rotation": 270}, "BACK": {"patternId": "M", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "G", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "M", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C220/initial_net.png", "targetTopFaceImage": "../images/C220/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 6, "targetRotationOffset": 180, "levelId": 220, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-220.json"}, "rollSequence": ["N", "S", "S", "E", "N", "W"], "observedPathFaces": [{"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "S", "S", "E", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "L", "rotation": 180}, "RIGHT": {"patternId": "Z", "rotation": 270}, "BACK": {"patternId": "M", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "G", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C220\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=M, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=M, rotation=270]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=Z, rotation=270]\n [FRONT: patternId=L, rotation=180]\n [BOTTOM: patternId=G, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=M, rotation=270\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=Z, rotation=270\n- FRONT: patternId=L, rotation=180\n- BOTTOM: patternId=G, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C220/initial_net.png", "targetTopFaceImage": "images/C220/target_top_face.png"}, "__sample_id__": "C220"} +{"taskType": "roll_to_target_top_face", "code": "C221", "name": "Goal Roll C221", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "plus", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "square", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "E", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "triangle", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "4", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "1", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "plus", "rotation": 270}, "FRONT": {"patternId": "square", "rotation": 180}, "RIGHT": {"patternId": "E", "rotation": 270}, "BACK": {"patternId": "triangle", "rotation": 0}, "LEFT": {"patternId": "4", "rotation": 180}, "BOTTOM": {"patternId": "1", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "plus", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C221/initial_net.png", "targetTopFaceImage": "../images/C221/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 4, "targetRotationOffset": 90, "levelId": 221, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-221.json"}, "rollSequence": ["W", "N", "N", "E", "N", "N"], "observedPathFaces": [{"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "N", "E", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "plus", "rotation": 270}, "FRONT": {"patternId": "square", "rotation": 180}, "RIGHT": {"patternId": "E", "rotation": 270}, "BACK": {"patternId": "triangle", "rotation": 0}, "LEFT": {"patternId": "4", "rotation": 180}, "BOTTOM": {"patternId": "1", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C221\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=plus, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=triangle, rotation=0]\n[LEFT: patternId=4, rotation=180] [TOP: patternId=plus, rotation=270] [RIGHT: patternId=E, rotation=270]\n [FRONT: patternId=square, rotation=180]\n [BOTTOM: patternId=1, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=triangle, rotation=0\n- LEFT: patternId=4, rotation=180\n- TOP: patternId=plus, rotation=270\n- RIGHT: patternId=E, rotation=270\n- FRONT: patternId=square, rotation=180\n- BOTTOM: patternId=1, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C221/initial_net.png", "targetTopFaceImage": "images/C221/target_top_face.png"}, "__sample_id__": "C221"} +{"taskType": "roll_to_target_top_face", "code": "C222", "name": "Goal Roll C222", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "C", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "star", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "H", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "T", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "7", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "S", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "C", "rotation": 270}, "FRONT": {"patternId": "star", "rotation": 0}, "RIGHT": {"patternId": "H", "rotation": 180}, "BACK": {"patternId": "T", "rotation": 90}, "LEFT": {"patternId": "7", "rotation": 270}, "BOTTOM": {"patternId": "S", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "star", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C222/initial_net.png", "targetTopFaceImage": "../images/C222/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 3, "targetRotationOffset": 270, "levelId": 222, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-222.json"}, "rollSequence": ["W", "W", "N", "W", "S", "W", "W"], "observedPathFaces": [{"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "N", "W", "S", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "C", "rotation": 270}, "FRONT": {"patternId": "star", "rotation": 0}, "RIGHT": {"patternId": "H", "rotation": 180}, "BACK": {"patternId": "T", "rotation": 90}, "LEFT": {"patternId": "7", "rotation": 270}, "BOTTOM": {"patternId": "S", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C222\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=star, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=T, rotation=90]\n[LEFT: patternId=7, rotation=270] [TOP: patternId=C, rotation=270] [RIGHT: patternId=H, rotation=180]\n [FRONT: patternId=star, rotation=0]\n [BOTTOM: patternId=S, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=T, rotation=90\n- LEFT: patternId=7, rotation=270\n- TOP: patternId=C, rotation=270\n- RIGHT: patternId=H, rotation=180\n- FRONT: patternId=star, rotation=0\n- BOTTOM: patternId=S, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C222/initial_net.png", "targetTopFaceImage": "images/C222/target_top_face.png"}, "__sample_id__": "C222"} +{"taskType": "roll_to_target_top_face", "code": "C223", "name": "Goal Roll C223", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "C", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "G", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "I", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "1", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "C", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "G", "rotation": 90}, "BACK": {"patternId": "I", "rotation": 90}, "LEFT": {"patternId": "1", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "G", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C223/initial_net.png", "targetTopFaceImage": "../images/C223/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 4, "targetRotationOffset": 180, "levelId": 223, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-223.json"}, "rollSequence": ["E", "E", "N", "E", "W", "S"], "observedPathFaces": [{"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "N", "E", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "C", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "G", "rotation": 90}, "BACK": {"patternId": "I", "rotation": 90}, "LEFT": {"patternId": "1", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C223\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=G, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=I, rotation=90]\n[LEFT: patternId=1, rotation=0] [TOP: patternId=C, rotation=270] [RIGHT: patternId=G, rotation=90]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=I, rotation=90\n- LEFT: patternId=1, rotation=0\n- TOP: patternId=C, rotation=270\n- RIGHT: patternId=G, rotation=90\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C223/initial_net.png", "targetTopFaceImage": "images/C223/target_top_face.png"}, "__sample_id__": "C223"} +{"taskType": "roll_to_target_top_face", "code": "C224", "name": "Goal Roll C224", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "smile", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "square", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "4", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "D", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "triangle", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "smile", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 180}, "RIGHT": {"patternId": "4", "rotation": 180}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "triangle", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "triangle", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C224/initial_net.png", "targetTopFaceImage": "../images/C224/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 5, "targetRotationOffset": 180, "levelId": 224, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-224.json"}, "rollSequence": ["N", "E", "S", "E", "E", "W"], "observedPathFaces": [{"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "S", "E", "E", "W"]}, "legacy_answer": {"TOP": {"patternId": "smile", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 180}, "RIGHT": {"patternId": "4", "rotation": 180}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "triangle", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C224\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=triangle, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=D, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=smile, rotation=0] [RIGHT: patternId=4, rotation=180]\n [FRONT: patternId=square, rotation=180]\n [BOTTOM: patternId=triangle, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=D, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=smile, rotation=0\n- RIGHT: patternId=4, rotation=180\n- FRONT: patternId=square, rotation=180\n- BOTTOM: patternId=triangle, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C224/initial_net.png", "targetTopFaceImage": "images/C224/target_top_face.png"}, "__sample_id__": "C224"} +{"taskType": "roll_to_target_top_face", "code": "C225", "name": "Goal Roll C225", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "Z", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "B", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "smile", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "H", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "U", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "O", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "Z", "rotation": 90}, "FRONT": {"patternId": "B", "rotation": 180}, "RIGHT": {"patternId": "smile", "rotation": 0}, "BACK": {"patternId": "H", "rotation": 270}, "LEFT": {"patternId": "U", "rotation": 90}, "BOTTOM": {"patternId": "O", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "U", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C225/initial_net.png", "targetTopFaceImage": "../images/C225/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 225, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-225.json"}, "rollSequence": ["E", "N", "N", "E", "N", "N"], "observedPathFaces": [{"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "N", "E", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "Z", "rotation": 90}, "FRONT": {"patternId": "B", "rotation": 180}, "RIGHT": {"patternId": "smile", "rotation": 0}, "BACK": {"patternId": "H", "rotation": 270}, "LEFT": {"patternId": "U", "rotation": 90}, "BOTTOM": {"patternId": "O", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C225\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=U, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=H, rotation=270]\n[LEFT: patternId=U, rotation=90] [TOP: patternId=Z, rotation=90] [RIGHT: patternId=smile, rotation=0]\n [FRONT: patternId=B, rotation=180]\n [BOTTOM: patternId=O, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=H, rotation=270\n- LEFT: patternId=U, rotation=90\n- TOP: patternId=Z, rotation=90\n- RIGHT: patternId=smile, rotation=0\n- FRONT: patternId=B, rotation=180\n- BOTTOM: patternId=O, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C225/initial_net.png", "targetTopFaceImage": "images/C225/target_top_face.png"}, "__sample_id__": "C225"} +{"taskType": "roll_to_target_top_face", "code": "C226", "name": "Goal Roll C226", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "star", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "6", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "2", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "3", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "star", "rotation": 90}, "FRONT": {"patternId": "6", "rotation": 180}, "RIGHT": {"patternId": "2", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "3", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "3", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C226/initial_net.png", "targetTopFaceImage": "../images/C226/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 2, "targetRotationOffset": 270, "levelId": 226, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-226.json"}, "rollSequence": ["S", "S", "E", "N", "S", "E"], "observedPathFaces": [{"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "E", "N", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "star", "rotation": 90}, "FRONT": {"patternId": "6", "rotation": 180}, "RIGHT": {"patternId": "2", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "3", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C226\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=3, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=star, rotation=90] [RIGHT: patternId=2, rotation=90]\n [FRONT: patternId=6, rotation=180]\n [BOTTOM: patternId=3, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=star, rotation=90\n- RIGHT: patternId=2, rotation=90\n- FRONT: patternId=6, rotation=180\n- BOTTOM: patternId=3, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C226/initial_net.png", "targetTopFaceImage": "images/C226/target_top_face.png"}, "__sample_id__": "C226"} +{"taskType": "roll_to_target_top_face", "code": "C227", "name": "Goal Roll C227", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "2", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "4", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "6", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "C", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "C", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 90}, "RIGHT": {"patternId": "4", "rotation": 0}, "BACK": {"patternId": "6", "rotation": 180}, "LEFT": {"patternId": "C", "rotation": 270}, "BOTTOM": {"patternId": "C", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "2", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C227/initial_net.png", "targetTopFaceImage": "../images/C227/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 4, "targetRotationOffset": 90, "levelId": 227, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-227.json"}, "rollSequence": ["S", "W", "N", "W", "E", "N"], "observedPathFaces": [{"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "N", "W", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 90}, "RIGHT": {"patternId": "4", "rotation": 0}, "BACK": {"patternId": "6", "rotation": 180}, "LEFT": {"patternId": "C", "rotation": 270}, "BOTTOM": {"patternId": "C", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C227\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=2, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=6, rotation=180]\n[LEFT: patternId=C, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=4, rotation=0]\n [FRONT: patternId=2, rotation=90]\n [BOTTOM: patternId=C, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=6, rotation=180\n- LEFT: patternId=C, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=4, rotation=0\n- FRONT: patternId=2, rotation=90\n- BOTTOM: patternId=C, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C227/initial_net.png", "targetTopFaceImage": "images/C227/target_top_face.png"}, "__sample_id__": "C227"} +{"taskType": "roll_to_target_top_face", "code": "C228", "name": "Goal Roll C228", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "star", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "Q", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "triangle", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "2", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "3", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "8", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "star", "rotation": 0}, "FRONT": {"patternId": "Q", "rotation": 270}, "RIGHT": {"patternId": "triangle", "rotation": 270}, "BACK": {"patternId": "2", "rotation": 270}, "LEFT": {"patternId": "3", "rotation": 90}, "BOTTOM": {"patternId": "8", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "star", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C228/initial_net.png", "targetTopFaceImage": "../images/C228/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 5, "targetRotationOffset": 270, "levelId": 228, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-228.json"}, "rollSequence": ["W", "W", "N", "W", "N", "W"], "observedPathFaces": [{"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "N", "W", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "star", "rotation": 0}, "FRONT": {"patternId": "Q", "rotation": 270}, "RIGHT": {"patternId": "triangle", "rotation": 270}, "BACK": {"patternId": "2", "rotation": 270}, "LEFT": {"patternId": "3", "rotation": 90}, "BOTTOM": {"patternId": "8", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C228\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=star, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=2, rotation=270]\n[LEFT: patternId=3, rotation=90] [TOP: patternId=star, rotation=0] [RIGHT: patternId=triangle, rotation=270]\n [FRONT: patternId=Q, rotation=270]\n [BOTTOM: patternId=8, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=2, rotation=270\n- LEFT: patternId=3, rotation=90\n- TOP: patternId=star, rotation=0\n- RIGHT: patternId=triangle, rotation=270\n- FRONT: patternId=Q, rotation=270\n- BOTTOM: patternId=8, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C228/initial_net.png", "targetTopFaceImage": "images/C228/target_top_face.png"}, "__sample_id__": "C228"} +{"taskType": "roll_to_target_top_face", "code": "C229", "name": "Goal Roll C229", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "Q", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "9", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "triangle", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "I", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "R", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "Q", "rotation": 270}, "FRONT": {"patternId": "9", "rotation": 0}, "RIGHT": {"patternId": "triangle", "rotation": 180}, "BACK": {"patternId": "I", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "R", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "R", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C229/initial_net.png", "targetTopFaceImage": "../images/C229/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 5, "targetRotationOffset": 270, "levelId": 229, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-229.json"}, "rollSequence": ["E", "W", "N", "E", "N", "E"], "observedPathFaces": [{"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "W", "N", "E", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "Q", "rotation": 270}, "FRONT": {"patternId": "9", "rotation": 0}, "RIGHT": {"patternId": "triangle", "rotation": 180}, "BACK": {"patternId": "I", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "R", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C229\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=R, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=I, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=Q, rotation=270] [RIGHT: patternId=triangle, rotation=180]\n [FRONT: patternId=9, rotation=0]\n [BOTTOM: patternId=R, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=I, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=Q, rotation=270\n- RIGHT: patternId=triangle, rotation=180\n- FRONT: patternId=9, rotation=0\n- BOTTOM: patternId=R, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C229/initial_net.png", "targetTopFaceImage": "images/C229/target_top_face.png"}, "__sample_id__": "C229"} +{"taskType": "roll_to_target_top_face", "code": "C230", "name": "Goal Roll C230", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "J", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "2", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "7", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "W", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "star", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "J", "rotation": 270}, "RIGHT": {"patternId": "2", "rotation": 270}, "BACK": {"patternId": "7", "rotation": 180}, "LEFT": {"patternId": "W", "rotation": 180}, "BOTTOM": {"patternId": "star", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "W", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C230/initial_net.png", "targetTopFaceImage": "../images/C230/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 2, "targetRotationOffset": 270, "levelId": 230, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-230.json"}, "rollSequence": ["N", "E", "W", "W", "W", "S"], "observedPathFaces": [{"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "W", "W", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "J", "rotation": 270}, "RIGHT": {"patternId": "2", "rotation": 270}, "BACK": {"patternId": "7", "rotation": 180}, "LEFT": {"patternId": "W", "rotation": 180}, "BOTTOM": {"patternId": "star", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C230\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=W, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=7, rotation=180]\n[LEFT: patternId=W, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=2, rotation=270]\n [FRONT: patternId=J, rotation=270]\n [BOTTOM: patternId=star, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=7, rotation=180\n- LEFT: patternId=W, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=2, rotation=270\n- FRONT: patternId=J, rotation=270\n- BOTTOM: patternId=star, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C230/initial_net.png", "targetTopFaceImage": "images/C230/target_top_face.png"}, "__sample_id__": "C230"} +{"taskType": "roll_to_target_top_face", "code": "C231", "name": "Goal Roll C231", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "1", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "heart", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "O", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "L", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "D", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "1", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 270}, "RIGHT": {"patternId": "O", "rotation": 0}, "BACK": {"patternId": "L", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "D", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "D", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C231/initial_net.png", "targetTopFaceImage": "../images/C231/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 2, "targetRotationOffset": 270, "levelId": 231, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-231.json"}, "rollSequence": ["N", "N", "S", "S", "E", "S", "N"], "observedPathFaces": [{"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "S", "S", "E", "S", "N"]}, "legacy_answer": {"TOP": {"patternId": "1", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 270}, "RIGHT": {"patternId": "O", "rotation": 0}, "BACK": {"patternId": "L", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "D", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C231\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=D, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=L, rotation=90]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=1, rotation=0] [RIGHT: patternId=O, rotation=0]\n [FRONT: patternId=heart, rotation=270]\n [BOTTOM: patternId=D, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=L, rotation=90\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=1, rotation=0\n- RIGHT: patternId=O, rotation=0\n- FRONT: patternId=heart, rotation=270\n- BOTTOM: patternId=D, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C231/initial_net.png", "targetTopFaceImage": "images/C231/target_top_face.png"}, "__sample_id__": "C231"} +{"taskType": "roll_to_target_top_face", "code": "C232", "name": "Goal Roll C232", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "triangle", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "4", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "plus", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "heart", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "F", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "triangle", "rotation": 270}, "FRONT": {"patternId": "4", "rotation": 0}, "RIGHT": {"patternId": "plus", "rotation": 180}, "BACK": {"patternId": "heart", "rotation": 270}, "LEFT": {"patternId": "F", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "F", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C232/initial_net.png", "targetTopFaceImage": "../images/C232/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 2, "targetRotationOffset": 270, "levelId": 232, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-232.json"}, "rollSequence": ["S", "E", "E", "S", "E", "N", "N"], "observedPathFaces": [{"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "E", "S", "E", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "triangle", "rotation": 270}, "FRONT": {"patternId": "4", "rotation": 0}, "RIGHT": {"patternId": "plus", "rotation": 180}, "BACK": {"patternId": "heart", "rotation": 270}, "LEFT": {"patternId": "F", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C232\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=F, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=heart, rotation=270]\n[LEFT: patternId=F, rotation=270] [TOP: patternId=triangle, rotation=270] [RIGHT: patternId=plus, rotation=180]\n [FRONT: patternId=4, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=heart, rotation=270\n- LEFT: patternId=F, rotation=270\n- TOP: patternId=triangle, rotation=270\n- RIGHT: patternId=plus, rotation=180\n- FRONT: patternId=4, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C232/initial_net.png", "targetTopFaceImage": "images/C232/target_top_face.png"}, "__sample_id__": "C232"} +{"taskType": "roll_to_target_top_face", "code": "C233", "name": "Goal Roll C233", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "square", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "P", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "Q", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "star", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "H", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "square", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "P", "rotation": 90}, "BACK": {"patternId": "Q", "rotation": 90}, "LEFT": {"patternId": "star", "rotation": 270}, "BOTTOM": {"patternId": "H", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "square", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C233/initial_net.png", "targetTopFaceImage": "../images/C233/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 6, "targetRotationOffset": 90, "levelId": 233, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-233.json"}, "rollSequence": ["N", "E", "N", "W", "N", "W", "W"], "observedPathFaces": [{"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "N", "W", "N", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "square", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "P", "rotation": 90}, "BACK": {"patternId": "Q", "rotation": 90}, "LEFT": {"patternId": "star", "rotation": 270}, "BOTTOM": {"patternId": "H", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C233\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=square, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=Q, rotation=90]\n[LEFT: patternId=star, rotation=270] [TOP: patternId=square, rotation=180] [RIGHT: patternId=P, rotation=90]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=H, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Q, rotation=90\n- LEFT: patternId=star, rotation=270\n- TOP: patternId=square, rotation=180\n- RIGHT: patternId=P, rotation=90\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=H, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C233/initial_net.png", "targetTopFaceImage": "images/C233/target_top_face.png"}, "__sample_id__": "C233"} +{"taskType": "roll_to_target_top_face", "code": "C234", "name": "Goal Roll C234", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "O", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "T", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "1", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "J", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "V", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "O", "rotation": 270}, "FRONT": {"patternId": "T", "rotation": 180}, "RIGHT": {"patternId": "1", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "J", "rotation": 90}, "BOTTOM": {"patternId": "V", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "V", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C234/initial_net.png", "targetTopFaceImage": "../images/C234/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 3, "targetRotationOffset": 90, "levelId": 234, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-234.json"}, "rollSequence": ["S", "E", "S", "W", "W", "S"], "observedPathFaces": [{"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "S", "W", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 270}, "FRONT": {"patternId": "T", "rotation": 180}, "RIGHT": {"patternId": "1", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "J", "rotation": 90}, "BOTTOM": {"patternId": "V", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C234\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=V, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=J, rotation=90] [TOP: patternId=O, rotation=270] [RIGHT: patternId=1, rotation=180]\n [FRONT: patternId=T, rotation=180]\n [BOTTOM: patternId=V, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=J, rotation=90\n- TOP: patternId=O, rotation=270\n- RIGHT: patternId=1, rotation=180\n- FRONT: patternId=T, rotation=180\n- BOTTOM: patternId=V, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C234/initial_net.png", "targetTopFaceImage": "images/C234/target_top_face.png"}, "__sample_id__": "C234"} +{"taskType": "roll_to_target_top_face", "code": "C235", "name": "Goal Roll C235", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "E", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "square", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "square", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "K", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "6", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "E", "rotation": 0}, "RIGHT": {"patternId": "square", "rotation": 0}, "BACK": {"patternId": "square", "rotation": 180}, "LEFT": {"patternId": "K", "rotation": 270}, "BOTTOM": {"patternId": "6", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 6, "stepNumber": 7, "patternId": "E", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C235/initial_net.png", "targetTopFaceImage": "../images/C235/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 7, "targetRotationOffset": 90, "levelId": 235, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-235.json"}, "rollSequence": ["S", "E", "N", "N", "E", "W", "E"], "observedPathFaces": [{"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "N", "N", "E", "W", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "E", "rotation": 0}, "RIGHT": {"patternId": "square", "rotation": 0}, "BACK": {"patternId": "square", "rotation": 180}, "LEFT": {"patternId": "K", "rotation": 270}, "BOTTOM": {"patternId": "6", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C235\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=E, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=square, rotation=180]\n[LEFT: patternId=K, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=square, rotation=0]\n [FRONT: patternId=E, rotation=0]\n [BOTTOM: patternId=6, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=square, rotation=180\n- LEFT: patternId=K, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=square, rotation=0\n- FRONT: patternId=E, rotation=0\n- BOTTOM: patternId=6, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C235/initial_net.png", "targetTopFaceImage": "images/C235/target_top_face.png"}, "__sample_id__": "C235"} +{"taskType": "roll_to_target_top_face", "code": "C236", "name": "Goal Roll C236", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "O", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "5", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "S", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "J", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "U", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "O", "rotation": 90}, "FRONT": {"patternId": "5", "rotation": 270}, "RIGHT": {"patternId": "S", "rotation": 180}, "BACK": {"patternId": "J", "rotation": 0}, "LEFT": {"patternId": "U", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "U", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C236/initial_net.png", "targetTopFaceImage": "../images/C236/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 236, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-236.json"}, "rollSequence": ["E", "N", "N", "E", "N", "S", "W"], "observedPathFaces": [{"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "N", "E", "N", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 90}, "FRONT": {"patternId": "5", "rotation": 270}, "RIGHT": {"patternId": "S", "rotation": 180}, "BACK": {"patternId": "J", "rotation": 0}, "LEFT": {"patternId": "U", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C236\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=U, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=J, rotation=0]\n[LEFT: patternId=U, rotation=270] [TOP: patternId=O, rotation=90] [RIGHT: patternId=S, rotation=180]\n [FRONT: patternId=5, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=J, rotation=0\n- LEFT: patternId=U, rotation=270\n- TOP: patternId=O, rotation=90\n- RIGHT: patternId=S, rotation=180\n- FRONT: patternId=5, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C236/initial_net.png", "targetTopFaceImage": "images/C236/target_top_face.png"}, "__sample_id__": "C236"} +{"taskType": "roll_to_target_top_face", "code": "C237", "name": "Goal Roll C237", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "2", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "2", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "6", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "N", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "2", "rotation": 270}, "FRONT": {"patternId": "2", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 90}, "BACK": {"patternId": "N", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "2", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C237/initial_net.png", "targetTopFaceImage": "../images/C237/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 3, "targetRotationOffset": 180, "levelId": 237, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-237.json"}, "rollSequence": ["S", "S", "S", "E", "N", "E", "W"], "observedPathFaces": [{"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "S", "E", "N", "E", "W"]}, "legacy_answer": {"TOP": {"patternId": "2", "rotation": 270}, "FRONT": {"patternId": "2", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 90}, "BACK": {"patternId": "N", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C237\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=2, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=N, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=2, rotation=270] [RIGHT: patternId=6, rotation=90]\n [FRONT: patternId=2, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=N, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=2, rotation=270\n- RIGHT: patternId=6, rotation=90\n- FRONT: patternId=2, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C237/initial_net.png", "targetTopFaceImage": "images/C237/target_top_face.png"}, "__sample_id__": "C237"} +{"taskType": "roll_to_target_top_face", "code": "C238", "name": "Goal Roll C238", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "N", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "triangle", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "V", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "U", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "M", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 90}, "RIGHT": {"patternId": "triangle", "rotation": 0}, "BACK": {"patternId": "V", "rotation": 180}, "LEFT": {"patternId": "U", "rotation": 180}, "BOTTOM": {"patternId": "M", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "U", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C238/initial_net.png", "targetTopFaceImage": "../images/C238/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 2, "targetRotationOffset": 270, "levelId": 238, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-238.json"}, "rollSequence": ["N", "E", "E", "E", "S", "N"], "observedPathFaces": [{"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "E", "E", "S", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 90}, "RIGHT": {"patternId": "triangle", "rotation": 0}, "BACK": {"patternId": "V", "rotation": 180}, "LEFT": {"patternId": "U", "rotation": 180}, "BOTTOM": {"patternId": "M", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C238\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=U, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=V, rotation=180]\n[LEFT: patternId=U, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=triangle, rotation=0]\n [FRONT: patternId=N, rotation=90]\n [BOTTOM: patternId=M, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=V, rotation=180\n- LEFT: patternId=U, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=triangle, rotation=0\n- FRONT: patternId=N, rotation=90\n- BOTTOM: patternId=M, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C238/initial_net.png", "targetTopFaceImage": "images/C238/target_top_face.png"}, "__sample_id__": "C238"} +{"taskType": "roll_to_target_top_face", "code": "C239", "name": "Goal Roll C239", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "B", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "5", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "C", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "Q", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "B", "rotation": 180}, "RIGHT": {"patternId": "5", "rotation": 270}, "BACK": {"patternId": "C", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "Q", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "B", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C239/initial_net.png", "targetTopFaceImage": "../images/C239/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 6, "targetRotationOffset": 90, "levelId": 239, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-239.json"}, "rollSequence": ["S", "E", "E", "N", "W", "S"], "observedPathFaces": [{"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "E", "N", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "B", "rotation": 180}, "RIGHT": {"patternId": "5", "rotation": 270}, "BACK": {"patternId": "C", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "Q", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C239\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=B, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=C, rotation=90]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=5, rotation=270]\n [FRONT: patternId=B, rotation=180]\n [BOTTOM: patternId=Q, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=C, rotation=90\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=5, rotation=270\n- FRONT: patternId=B, rotation=180\n- BOTTOM: patternId=Q, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C239/initial_net.png", "targetTopFaceImage": "images/C239/target_top_face.png"}, "__sample_id__": "C239"} +{"taskType": "roll_to_target_top_face", "code": "C240", "name": "Goal Roll C240", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "H", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "Y", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_right", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_left", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "P", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "H", "rotation": 270}, "FRONT": {"patternId": "Y", "rotation": 270}, "RIGHT": {"patternId": "arrow_right", "rotation": 90}, "BACK": {"patternId": "arrow_left", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "P", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "Y", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C240/initial_net.png", "targetTopFaceImage": "../images/C240/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 240, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-240.json"}, "rollSequence": ["N", "S", "E", "E", "S", "W"], "observedPathFaces": [{"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "S", "E", "E", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "H", "rotation": 270}, "FRONT": {"patternId": "Y", "rotation": 270}, "RIGHT": {"patternId": "arrow_right", "rotation": 90}, "BACK": {"patternId": "arrow_left", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "P", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C240\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=Y, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_left, rotation=270]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=H, rotation=270] [RIGHT: patternId=arrow_right, rotation=90]\n [FRONT: patternId=Y, rotation=270]\n [BOTTOM: patternId=P, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_left, rotation=270\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=H, rotation=270\n- RIGHT: patternId=arrow_right, rotation=90\n- FRONT: patternId=Y, rotation=270\n- BOTTOM: patternId=P, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C240/initial_net.png", "targetTopFaceImage": "images/C240/target_top_face.png"}, "__sample_id__": "C240"} +{"taskType": "roll_to_target_top_face", "code": "C241", "name": "Goal Roll C241", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "F", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "G", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "E", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "J", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "C", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "F", "rotation": 270}, "FRONT": {"patternId": "G", "rotation": 270}, "RIGHT": {"patternId": "E", "rotation": 90}, "BACK": {"patternId": "J", "rotation": 180}, "LEFT": {"patternId": "C", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "C", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C241/initial_net.png", "targetTopFaceImage": "../images/C241/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 5, "targetRotationOffset": 180, "levelId": 241, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-241.json"}, "rollSequence": ["N", "W", "W", "N", "W", "S", "N"], "observedPathFaces": [{"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "W", "N", "W", "S", "N"]}, "legacy_answer": {"TOP": {"patternId": "F", "rotation": 270}, "FRONT": {"patternId": "G", "rotation": 270}, "RIGHT": {"patternId": "E", "rotation": 90}, "BACK": {"patternId": "J", "rotation": 180}, "LEFT": {"patternId": "C", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C241\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=C, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=J, rotation=180]\n[LEFT: patternId=C, rotation=0] [TOP: patternId=F, rotation=270] [RIGHT: patternId=E, rotation=90]\n [FRONT: patternId=G, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=J, rotation=180\n- LEFT: patternId=C, rotation=0\n- TOP: patternId=F, rotation=270\n- RIGHT: patternId=E, rotation=90\n- FRONT: patternId=G, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C241/initial_net.png", "targetTopFaceImage": "images/C241/target_top_face.png"}, "__sample_id__": "C241"} +{"taskType": "roll_to_target_top_face", "code": "C242", "name": "Goal Roll C242", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "J", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "E", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "Z", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "E", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "2", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "J", "rotation": 270}, "RIGHT": {"patternId": "E", "rotation": 90}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "E", "rotation": 180}, "BOTTOM": {"patternId": "2", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "J", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C242/initial_net.png", "targetTopFaceImage": "../images/C242/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 4, "targetRotationOffset": 90, "levelId": 242, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-242.json"}, "rollSequence": ["W", "E", "E", "N", "N", "N"], "observedPathFaces": [{"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "E", "E", "N", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "J", "rotation": 270}, "RIGHT": {"patternId": "E", "rotation": 90}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "E", "rotation": 180}, "BOTTOM": {"patternId": "2", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C242\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=J, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=Z, rotation=90]\n[LEFT: patternId=E, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=E, rotation=90]\n [FRONT: patternId=J, rotation=270]\n [BOTTOM: patternId=2, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Z, rotation=90\n- LEFT: patternId=E, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=E, rotation=90\n- FRONT: patternId=J, rotation=270\n- BOTTOM: patternId=2, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C242/initial_net.png", "targetTopFaceImage": "images/C242/target_top_face.png"}, "__sample_id__": "C242"} +{"taskType": "roll_to_target_top_face", "code": "C243", "name": "Goal Roll C243", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "B", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "O", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "5", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "8", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_down", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "B", "rotation": 270}, "FRONT": {"patternId": "O", "rotation": 90}, "RIGHT": {"patternId": "5", "rotation": 180}, "BACK": {"patternId": "8", "rotation": 90}, "LEFT": {"patternId": "arrow_down", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "O", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C243/initial_net.png", "targetTopFaceImage": "../images/C243/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 6, "targetRotationOffset": 270, "levelId": 243, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-243.json"}, "rollSequence": ["W", "W", "S", "W", "N", "W"], "observedPathFaces": [{"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "S", "W", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "B", "rotation": 270}, "FRONT": {"patternId": "O", "rotation": 90}, "RIGHT": {"patternId": "5", "rotation": 180}, "BACK": {"patternId": "8", "rotation": 90}, "LEFT": {"patternId": "arrow_down", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C243\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=O, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=8, rotation=90]\n[LEFT: patternId=arrow_down, rotation=270] [TOP: patternId=B, rotation=270] [RIGHT: patternId=5, rotation=180]\n [FRONT: patternId=O, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=8, rotation=90\n- LEFT: patternId=arrow_down, rotation=270\n- TOP: patternId=B, rotation=270\n- RIGHT: patternId=5, rotation=180\n- FRONT: patternId=O, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C243/initial_net.png", "targetTopFaceImage": "images/C243/target_top_face.png"}, "__sample_id__": "C243"} +{"taskType": "roll_to_target_top_face", "code": "C244", "name": "Goal Roll C244", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "L", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "B", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "X", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "X", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "square", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "L", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "B", "rotation": 0}, "BACK": {"patternId": "X", "rotation": 0}, "LEFT": {"patternId": "X", "rotation": 0}, "BOTTOM": {"patternId": "square", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "square", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C244/initial_net.png", "targetTopFaceImage": "../images/C244/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 5, "targetRotationOffset": 270, "levelId": 244, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-244.json"}, "rollSequence": ["E", "N", "W", "N", "N", "E"], "observedPathFaces": [{"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "W", "N", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "L", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "B", "rotation": 0}, "BACK": {"patternId": "X", "rotation": 0}, "LEFT": {"patternId": "X", "rotation": 0}, "BOTTOM": {"patternId": "square", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C244\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=square, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=X, rotation=0]\n[LEFT: patternId=X, rotation=0] [TOP: patternId=L, rotation=90] [RIGHT: patternId=B, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=square, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=X, rotation=0\n- LEFT: patternId=X, rotation=0\n- TOP: patternId=L, rotation=90\n- RIGHT: patternId=B, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=square, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C244/initial_net.png", "targetTopFaceImage": "images/C244/target_top_face.png"}, "__sample_id__": "C244"} +{"taskType": "roll_to_target_top_face", "code": "C245", "name": "Goal Roll C245", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "3", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "I", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "K", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "D", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "plus", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "3", "rotation": 270}, "FRONT": {"patternId": "I", "rotation": 270}, "RIGHT": {"patternId": "K", "rotation": 90}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "plus", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "plus", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C245/initial_net.png", "targetTopFaceImage": "../images/C245/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 3, "targetRotationOffset": 270, "levelId": 245, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-245.json"}, "rollSequence": ["E", "S", "E", "N", "N", "E"], "observedPathFaces": [{"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "E", "N", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "3", "rotation": 270}, "FRONT": {"patternId": "I", "rotation": 270}, "RIGHT": {"patternId": "K", "rotation": 90}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "plus", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C245\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=plus, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=D, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=3, rotation=270] [RIGHT: patternId=K, rotation=90]\n [FRONT: patternId=I, rotation=270]\n [BOTTOM: patternId=plus, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=D, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=3, rotation=270\n- RIGHT: patternId=K, rotation=90\n- FRONT: patternId=I, rotation=270\n- BOTTOM: patternId=plus, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C245/initial_net.png", "targetTopFaceImage": "images/C245/target_top_face.png"}, "__sample_id__": "C245"} +{"taskType": "roll_to_target_top_face", "code": "C246", "name": "Goal Roll C246", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "M", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "heart", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "M", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "4", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "diamond", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "M", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 0}, "RIGHT": {"patternId": "M", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "4", "rotation": 270}, "BOTTOM": {"patternId": "diamond", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "M", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C246/initial_net.png", "targetTopFaceImage": "../images/C246/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 4, "targetRotationOffset": 90, "levelId": 246, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-246.json"}, "rollSequence": ["S", "S", "W", "W", "E", "N", "N"], "observedPathFaces": [{"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "W", "W", "E", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "M", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 0}, "RIGHT": {"patternId": "M", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "4", "rotation": 270}, "BOTTOM": {"patternId": "diamond", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C246\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=M, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=4, rotation=270] [TOP: patternId=M, rotation=0] [RIGHT: patternId=M, rotation=0]\n [FRONT: patternId=heart, rotation=0]\n [BOTTOM: patternId=diamond, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=4, rotation=270\n- TOP: patternId=M, rotation=0\n- RIGHT: patternId=M, rotation=0\n- FRONT: patternId=heart, rotation=0\n- BOTTOM: patternId=diamond, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C246/initial_net.png", "targetTopFaceImage": "images/C246/target_top_face.png"}, "__sample_id__": "C246"} +{"taskType": "roll_to_target_top_face", "code": "C247", "name": "Goal Roll C247", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "4", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "5", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "F", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "N", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "4", "rotation": 90}, "FRONT": {"patternId": "5", "rotation": 0}, "RIGHT": {"patternId": "F", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "N", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "F", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C247/initial_net.png", "targetTopFaceImage": "../images/C247/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 3, "targetRotationOffset": 270, "levelId": 247, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-247.json"}, "rollSequence": ["E", "S", "S", "E", "N", "W", "S"], "observedPathFaces": [{"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "S", "E", "N", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "4", "rotation": 90}, "FRONT": {"patternId": "5", "rotation": 0}, "RIGHT": {"patternId": "F", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "N", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C247\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=F, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=N, rotation=90] [TOP: patternId=4, rotation=90] [RIGHT: patternId=F, rotation=0]\n [FRONT: patternId=5, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=N, rotation=90\n- TOP: patternId=4, rotation=90\n- RIGHT: patternId=F, rotation=0\n- FRONT: patternId=5, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C247/initial_net.png", "targetTopFaceImage": "images/C247/target_top_face.png"}, "__sample_id__": "C247"} +{"taskType": "roll_to_target_top_face", "code": "C248", "name": "Goal Roll C248", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "F", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "square", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_up", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "star", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "P", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "W", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "F", "rotation": 180}, "FRONT": {"patternId": "square", "rotation": 270}, "RIGHT": {"patternId": "arrow_up", "rotation": 180}, "BACK": {"patternId": "star", "rotation": 0}, "LEFT": {"patternId": "P", "rotation": 180}, "BOTTOM": {"patternId": "W", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "square", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C248/initial_net.png", "targetTopFaceImage": "../images/C248/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 248, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-248.json"}, "rollSequence": ["N", "E", "E", "N", "N", "N", "E"], "observedPathFaces": [{"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "E", "N", "N", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "F", "rotation": 180}, "FRONT": {"patternId": "square", "rotation": 270}, "RIGHT": {"patternId": "arrow_up", "rotation": 180}, "BACK": {"patternId": "star", "rotation": 0}, "LEFT": {"patternId": "P", "rotation": 180}, "BOTTOM": {"patternId": "W", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C248\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=square, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=star, rotation=0]\n[LEFT: patternId=P, rotation=180] [TOP: patternId=F, rotation=180] [RIGHT: patternId=arrow_up, rotation=180]\n [FRONT: patternId=square, rotation=270]\n [BOTTOM: patternId=W, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=star, rotation=0\n- LEFT: patternId=P, rotation=180\n- TOP: patternId=F, rotation=180\n- RIGHT: patternId=arrow_up, rotation=180\n- FRONT: patternId=square, rotation=270\n- BOTTOM: patternId=W, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C248/initial_net.png", "targetTopFaceImage": "images/C248/target_top_face.png"}, "__sample_id__": "C248"} +{"taskType": "roll_to_target_top_face", "code": "C249", "name": "Goal Roll C249", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "2", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "X", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "O", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "heart", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_right", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "2", "rotation": 90}, "FRONT": {"patternId": "X", "rotation": 90}, "RIGHT": {"patternId": "O", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "heart", "rotation": 270}, "BOTTOM": {"patternId": "arrow_right", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 6, "stepNumber": 7, "patternId": "arrow_right", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C249/initial_net.png", "targetTopFaceImage": "../images/C249/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 7, "targetRotationOffset": 180, "levelId": 249, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-249.json"}, "rollSequence": ["W", "W", "W", "S", "W", "E", "E"], "observedPathFaces": [{"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "W", "S", "W", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "2", "rotation": 90}, "FRONT": {"patternId": "X", "rotation": 90}, "RIGHT": {"patternId": "O", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "heart", "rotation": 270}, "BOTTOM": {"patternId": "arrow_right", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C249\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=arrow_right, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=heart, rotation=270] [TOP: patternId=2, rotation=90] [RIGHT: patternId=O, rotation=90]\n [FRONT: patternId=X, rotation=90]\n [BOTTOM: patternId=arrow_right, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=heart, rotation=270\n- TOP: patternId=2, rotation=90\n- RIGHT: patternId=O, rotation=90\n- FRONT: patternId=X, rotation=90\n- BOTTOM: patternId=arrow_right, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C249/initial_net.png", "targetTopFaceImage": "images/C249/target_top_face.png"}, "__sample_id__": "C249"} +{"taskType": "roll_to_target_top_face", "code": "C250", "name": "Goal Roll C250", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "B", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "1", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "O", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "smile", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "M", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "2", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "B", "rotation": 0}, "FRONT": {"patternId": "1", "rotation": 0}, "RIGHT": {"patternId": "O", "rotation": 90}, "BACK": {"patternId": "smile", "rotation": 90}, "LEFT": {"patternId": "M", "rotation": 270}, "BOTTOM": {"patternId": "2", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 6, "stepNumber": 7, "patternId": "2", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C250/initial_net.png", "targetTopFaceImage": "../images/C250/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 7, "targetRotationOffset": 180, "levelId": 250, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-250.json"}, "rollSequence": ["E", "N", "N", "W", "N", "W", "N"], "observedPathFaces": [{"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "N", "W", "N", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "B", "rotation": 0}, "FRONT": {"patternId": "1", "rotation": 0}, "RIGHT": {"patternId": "O", "rotation": 90}, "BACK": {"patternId": "smile", "rotation": 90}, "LEFT": {"patternId": "M", "rotation": 270}, "BOTTOM": {"patternId": "2", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C250\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=2, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=smile, rotation=90]\n[LEFT: patternId=M, rotation=270] [TOP: patternId=B, rotation=0] [RIGHT: patternId=O, rotation=90]\n [FRONT: patternId=1, rotation=0]\n [BOTTOM: patternId=2, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=smile, rotation=90\n- LEFT: patternId=M, rotation=270\n- TOP: patternId=B, rotation=0\n- RIGHT: patternId=O, rotation=90\n- FRONT: patternId=1, rotation=0\n- BOTTOM: patternId=2, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C250/initial_net.png", "targetTopFaceImage": "images/C250/target_top_face.png"}, "__sample_id__": "C250"} +{"taskType": "roll_to_target_top_face", "code": "C251", "name": "Goal Roll C251", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "D", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "9", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "V", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "H", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "D", "rotation": 180}, "BACK": {"patternId": "9", "rotation": 180}, "LEFT": {"patternId": "V", "rotation": 90}, "BOTTOM": {"patternId": "H", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "V", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C251/initial_net.png", "targetTopFaceImage": "../images/C251/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 2, "targetRotationOffset": 180, "levelId": 251, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-251.json"}, "rollSequence": ["N", "E", "W", "W", "S", "S"], "observedPathFaces": [{"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "W", "W", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "D", "rotation": 180}, "BACK": {"patternId": "9", "rotation": 180}, "LEFT": {"patternId": "V", "rotation": 90}, "BOTTOM": {"patternId": "H", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C251\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=V, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=9, rotation=180]\n[LEFT: patternId=V, rotation=90] [TOP: patternId=?, rotation=0] [RIGHT: patternId=D, rotation=180]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=H, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=9, rotation=180\n- LEFT: patternId=V, rotation=90\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=D, rotation=180\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=H, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C251/initial_net.png", "targetTopFaceImage": "images/C251/target_top_face.png"}, "__sample_id__": "C251"} +{"taskType": "roll_to_target_top_face", "code": "C252", "name": "Goal Roll C252", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "O", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "C", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "I", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "smile", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "A", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "O", "rotation": 0}, "FRONT": {"patternId": "C", "rotation": 90}, "RIGHT": {"patternId": "I", "rotation": 270}, "BACK": {"patternId": "smile", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "A", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "A", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C252/initial_net.png", "targetTopFaceImage": "../images/C252/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 6, "targetRotationOffset": 90, "levelId": 252, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-252.json"}, "rollSequence": ["N", "S", "S", "S", "E", "W"], "observedPathFaces": [{"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "S", "S", "S", "E", "W"]}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 0}, "FRONT": {"patternId": "C", "rotation": 90}, "RIGHT": {"patternId": "I", "rotation": 270}, "BACK": {"patternId": "smile", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "A", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C252\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=A, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=smile, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=O, rotation=0] [RIGHT: patternId=I, rotation=270]\n [FRONT: patternId=C, rotation=90]\n [BOTTOM: patternId=A, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=smile, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=O, rotation=0\n- RIGHT: patternId=I, rotation=270\n- FRONT: patternId=C, rotation=90\n- BOTTOM: patternId=A, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C252/initial_net.png", "targetTopFaceImage": "images/C252/target_top_face.png"}, "__sample_id__": "C252"} +{"taskType": "roll_to_target_top_face", "code": "C253", "name": "Goal Roll C253", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "4", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "plus", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "B", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "6", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "H", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "4", "rotation": 270}, "FRONT": {"patternId": "plus", "rotation": 90}, "RIGHT": {"patternId": "B", "rotation": 90}, "BACK": {"patternId": "6", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "H", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "plus", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C253/initial_net.png", "targetTopFaceImage": "../images/C253/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 253, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-253.json"}, "rollSequence": ["N", "N", "E", "E", "N", "N", "W"], "observedPathFaces": [{"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "E", "E", "N", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "4", "rotation": 270}, "FRONT": {"patternId": "plus", "rotation": 90}, "RIGHT": {"patternId": "B", "rotation": 90}, "BACK": {"patternId": "6", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "H", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C253\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=plus, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=6, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=4, rotation=270] [RIGHT: patternId=B, rotation=90]\n [FRONT: patternId=plus, rotation=90]\n [BOTTOM: patternId=H, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=6, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=4, rotation=270\n- RIGHT: patternId=B, rotation=90\n- FRONT: patternId=plus, rotation=90\n- BOTTOM: patternId=H, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C253/initial_net.png", "targetTopFaceImage": "images/C253/target_top_face.png"}, "__sample_id__": "C253"} +{"taskType": "roll_to_target_top_face", "code": "C254", "name": "Goal Roll C254", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "star", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "4", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "circle", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "heart", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "star", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "star", "rotation": 270}, "FRONT": {"patternId": "4", "rotation": 180}, "RIGHT": {"patternId": "circle", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "heart", "rotation": 90}, "BOTTOM": {"patternId": "star", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "star", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C254/initial_net.png", "targetTopFaceImage": "../images/C254/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 2, "targetRotationOffset": 90, "levelId": 254, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-254.json"}, "rollSequence": ["E", "W", "S", "E", "S", "S"], "observedPathFaces": [{"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "W", "S", "E", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "star", "rotation": 270}, "FRONT": {"patternId": "4", "rotation": 180}, "RIGHT": {"patternId": "circle", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "heart", "rotation": 90}, "BOTTOM": {"patternId": "star", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C254\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=star, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=heart, rotation=90] [TOP: patternId=star, rotation=270] [RIGHT: patternId=circle, rotation=90]\n [FRONT: patternId=4, rotation=180]\n [BOTTOM: patternId=star, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=heart, rotation=90\n- TOP: patternId=star, rotation=270\n- RIGHT: patternId=circle, rotation=90\n- FRONT: patternId=4, rotation=180\n- BOTTOM: patternId=star, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C254/initial_net.png", "targetTopFaceImage": "images/C254/target_top_face.png"}, "__sample_id__": "C254"} +{"taskType": "roll_to_target_top_face", "code": "C255", "name": "Goal Roll C255", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "3", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "9", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_down", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "I", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "4", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "3", "rotation": 270}, "FRONT": {"patternId": "9", "rotation": 270}, "RIGHT": {"patternId": "arrow_down", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "I", "rotation": 90}, "BOTTOM": {"patternId": "4", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "4", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C255/initial_net.png", "targetTopFaceImage": "../images/C255/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 4, "targetRotationOffset": 90, "levelId": 255, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-255.json"}, "rollSequence": ["S", "S", "W", "E", "E", "E"], "observedPathFaces": [{"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "W", "E", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "3", "rotation": 270}, "FRONT": {"patternId": "9", "rotation": 270}, "RIGHT": {"patternId": "arrow_down", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "I", "rotation": 90}, "BOTTOM": {"patternId": "4", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C255\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=4, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=I, rotation=90] [TOP: patternId=3, rotation=270] [RIGHT: patternId=arrow_down, rotation=0]\n [FRONT: patternId=9, rotation=270]\n [BOTTOM: patternId=4, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=I, rotation=90\n- TOP: patternId=3, rotation=270\n- RIGHT: patternId=arrow_down, rotation=0\n- FRONT: patternId=9, rotation=270\n- BOTTOM: patternId=4, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C255/initial_net.png", "targetTopFaceImage": "images/C255/target_top_face.png"}, "__sample_id__": "C255"} +{"taskType": "roll_to_target_top_face", "code": "C256", "name": "Goal Roll C256", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "R", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "R", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "X", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "Z", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "R", "rotation": 0}, "RIGHT": {"patternId": "R", "rotation": 270}, "BACK": {"patternId": "X", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "Z", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "X", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C256/initial_net.png", "targetTopFaceImage": "../images/C256/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 256, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-256.json"}, "rollSequence": ["S", "N", "E", "S", "W", "W"], "observedPathFaces": [{"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "N", "E", "S", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "R", "rotation": 0}, "RIGHT": {"patternId": "R", "rotation": 270}, "BACK": {"patternId": "X", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "Z", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C256\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=X, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=X, rotation=270]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=R, rotation=270]\n [FRONT: patternId=R, rotation=0]\n [BOTTOM: patternId=Z, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=X, rotation=270\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=R, rotation=270\n- FRONT: patternId=R, rotation=0\n- BOTTOM: patternId=Z, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C256/initial_net.png", "targetTopFaceImage": "images/C256/target_top_face.png"}, "__sample_id__": "C256"} +{"taskType": "roll_to_target_top_face", "code": "C257", "name": "Goal Roll C257", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "heart", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "M", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_left", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "6", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "S", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 180}, "RIGHT": {"patternId": "M", "rotation": 90}, "BACK": {"patternId": "arrow_left", "rotation": 90}, "LEFT": {"patternId": "6", "rotation": 180}, "BOTTOM": {"patternId": "S", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "6", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C257/initial_net.png", "targetTopFaceImage": "../images/C257/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 6, "targetRotationOffset": 180, "levelId": 257, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-257.json"}, "rollSequence": ["W", "S", "S", "S", "E", "N", "E"], "observedPathFaces": [{"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "S", "S", "E", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 180}, "RIGHT": {"patternId": "M", "rotation": 90}, "BACK": {"patternId": "arrow_left", "rotation": 90}, "LEFT": {"patternId": "6", "rotation": 180}, "BOTTOM": {"patternId": "S", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C257\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=6, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_left, rotation=90]\n[LEFT: patternId=6, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=M, rotation=90]\n [FRONT: patternId=heart, rotation=180]\n [BOTTOM: patternId=S, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_left, rotation=90\n- LEFT: patternId=6, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=M, rotation=90\n- FRONT: patternId=heart, rotation=180\n- BOTTOM: patternId=S, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C257/initial_net.png", "targetTopFaceImage": "images/C257/target_top_face.png"}, "__sample_id__": "C257"} +{"taskType": "roll_to_target_top_face", "code": "C258", "name": "Goal Roll C258", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "E", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "W", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "1", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "U", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "H", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "E", "rotation": 90}, "FRONT": {"patternId": "W", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 270}, "BACK": {"patternId": "U", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "H", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "E", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C258/initial_net.png", "targetTopFaceImage": "../images/C258/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 5, "targetRotationOffset": 180, "levelId": 258, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-258.json"}, "rollSequence": ["S", "E", "S", "N", "N", "E"], "observedPathFaces": [{"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "S", "N", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "E", "rotation": 90}, "FRONT": {"patternId": "W", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 270}, "BACK": {"patternId": "U", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "H", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C258\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=E, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=U, rotation=90]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=E, rotation=90] [RIGHT: patternId=1, rotation=270]\n [FRONT: patternId=W, rotation=0]\n [BOTTOM: patternId=H, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=U, rotation=90\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=E, rotation=90\n- RIGHT: patternId=1, rotation=270\n- FRONT: patternId=W, rotation=0\n- BOTTOM: patternId=H, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C258/initial_net.png", "targetTopFaceImage": "images/C258/target_top_face.png"}, "__sample_id__": "C258"} +{"taskType": "roll_to_target_top_face", "code": "C259", "name": "Goal Roll C259", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "L", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "E", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "M", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "8", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_down", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "L", "rotation": 180}, "RIGHT": {"patternId": "E", "rotation": 90}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 270}, "BOTTOM": {"patternId": "arrow_down", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "8", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C259/initial_net.png", "targetTopFaceImage": "../images/C259/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 6, "targetRotationOffset": 270, "levelId": 259, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-259.json"}, "rollSequence": ["W", "E", "S", "W", "E", "E", "E"], "observedPathFaces": [{"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "E", "S", "W", "E", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "L", "rotation": 180}, "RIGHT": {"patternId": "E", "rotation": 90}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 270}, "BOTTOM": {"patternId": "arrow_down", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C259\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=8, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=M, rotation=0]\n[LEFT: patternId=8, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=E, rotation=90]\n [FRONT: patternId=L, rotation=180]\n [BOTTOM: patternId=arrow_down, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=M, rotation=0\n- LEFT: patternId=8, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=E, rotation=90\n- FRONT: patternId=L, rotation=180\n- BOTTOM: patternId=arrow_down, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C259/initial_net.png", "targetTopFaceImage": "images/C259/target_top_face.png"}, "__sample_id__": "C259"} +{"taskType": "roll_to_target_top_face", "code": "C260", "name": "Goal Roll C260", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "9", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "C", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "circle", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "triangle", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "U", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "A", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "9", "rotation": 90}, "FRONT": {"patternId": "C", "rotation": 180}, "RIGHT": {"patternId": "circle", "rotation": 90}, "BACK": {"patternId": "triangle", "rotation": 90}, "LEFT": {"patternId": "U", "rotation": 270}, "BOTTOM": {"patternId": "A", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "C", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C260/initial_net.png", "targetTopFaceImage": "../images/C260/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 6, "targetRotationOffset": 180, "levelId": 260, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-260.json"}, "rollSequence": ["N", "W", "S", "W", "S", "S", "W"], "observedPathFaces": [{"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "S", "W", "S", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "9", "rotation": 90}, "FRONT": {"patternId": "C", "rotation": 180}, "RIGHT": {"patternId": "circle", "rotation": 90}, "BACK": {"patternId": "triangle", "rotation": 90}, "LEFT": {"patternId": "U", "rotation": 270}, "BOTTOM": {"patternId": "A", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C260\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=C, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=triangle, rotation=90]\n[LEFT: patternId=U, rotation=270] [TOP: patternId=9, rotation=90] [RIGHT: patternId=circle, rotation=90]\n [FRONT: patternId=C, rotation=180]\n [BOTTOM: patternId=A, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=triangle, rotation=90\n- LEFT: patternId=U, rotation=270\n- TOP: patternId=9, rotation=90\n- RIGHT: patternId=circle, rotation=90\n- FRONT: patternId=C, rotation=180\n- BOTTOM: patternId=A, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C260/initial_net.png", "targetTopFaceImage": "images/C260/target_top_face.png"}, "__sample_id__": "C260"} +{"taskType": "roll_to_target_top_face", "code": "C261", "name": "Goal Roll C261", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "arrow_up", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "I", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "5", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "L", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "J", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "arrow_up", "rotation": 270}, "FRONT": {"patternId": "I", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "5", "rotation": 90}, "LEFT": {"patternId": "L", "rotation": 270}, "BOTTOM": {"patternId": "J", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "5", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C261/initial_net.png", "targetTopFaceImage": "../images/C261/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 4, "targetRotationOffset": 270, "levelId": 261, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-261.json"}, "rollSequence": ["S", "S", "W", "N", "W", "W", "W"], "observedPathFaces": [{"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "W", "N", "W", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "arrow_up", "rotation": 270}, "FRONT": {"patternId": "I", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "5", "rotation": 90}, "LEFT": {"patternId": "L", "rotation": 270}, "BOTTOM": {"patternId": "J", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C261\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=5, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=5, rotation=90]\n[LEFT: patternId=L, rotation=270] [TOP: patternId=arrow_up, rotation=270] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=I, rotation=90]\n [BOTTOM: patternId=J, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=5, rotation=90\n- LEFT: patternId=L, rotation=270\n- TOP: patternId=arrow_up, rotation=270\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=I, rotation=90\n- BOTTOM: patternId=J, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C261/initial_net.png", "targetTopFaceImage": "images/C261/target_top_face.png"}, "__sample_id__": "C261"} +{"taskType": "roll_to_target_top_face", "code": "C262", "name": "Goal Roll C262", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "8", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "I", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "M", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "star", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "3", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "8", "rotation": 90}, "FRONT": {"patternId": "I", "rotation": 90}, "RIGHT": {"patternId": "M", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "star", "rotation": 90}, "BOTTOM": {"patternId": "3", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "8", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C262/initial_net.png", "targetTopFaceImage": "../images/C262/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 3, "targetRotationOffset": 180, "levelId": 262, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-262.json"}, "rollSequence": ["E", "S", "W", "S", "E", "W", "S"], "observedPathFaces": [{"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "W", "S", "E", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "8", "rotation": 90}, "FRONT": {"patternId": "I", "rotation": 90}, "RIGHT": {"patternId": "M", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "star", "rotation": 90}, "BOTTOM": {"patternId": "3", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C262\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=8, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=star, rotation=90] [TOP: patternId=8, rotation=90] [RIGHT: patternId=M, rotation=180]\n [FRONT: patternId=I, rotation=90]\n [BOTTOM: patternId=3, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=star, rotation=90\n- TOP: patternId=8, rotation=90\n- RIGHT: patternId=M, rotation=180\n- FRONT: patternId=I, rotation=90\n- BOTTOM: patternId=3, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C262/initial_net.png", "targetTopFaceImage": "images/C262/target_top_face.png"}, "__sample_id__": "C262"} +{"taskType": "roll_to_target_top_face", "code": "C263", "name": "Goal Roll C263", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "heart", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "9", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "6", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "heart", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "K", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "heart", "rotation": 180}, "FRONT": {"patternId": "9", "rotation": 180}, "RIGHT": {"patternId": "6", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "heart", "rotation": 180}, "BOTTOM": {"patternId": "K", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "heart", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C263/initial_net.png", "targetTopFaceImage": "../images/C263/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 3, "targetRotationOffset": 180, "levelId": 263, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-263.json"}, "rollSequence": ["S", "W", "N", "E", "N", "E"], "observedPathFaces": [{"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "N", "E", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "heart", "rotation": 180}, "FRONT": {"patternId": "9", "rotation": 180}, "RIGHT": {"patternId": "6", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "heart", "rotation": 180}, "BOTTOM": {"patternId": "K", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C263\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=heart, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=heart, rotation=180] [TOP: patternId=heart, rotation=180] [RIGHT: patternId=6, rotation=0]\n [FRONT: patternId=9, rotation=180]\n [BOTTOM: patternId=K, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=heart, rotation=180\n- TOP: patternId=heart, rotation=180\n- RIGHT: patternId=6, rotation=0\n- FRONT: patternId=9, rotation=180\n- BOTTOM: patternId=K, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C263/initial_net.png", "targetTopFaceImage": "images/C263/target_top_face.png"}, "__sample_id__": "C263"} +{"taskType": "roll_to_target_top_face", "code": "C264", "name": "Goal Roll C264", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "E", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "R", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "R", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "R", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_up", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "E", "rotation": 180}, "RIGHT": {"patternId": "R", "rotation": 270}, "BACK": {"patternId": "R", "rotation": 270}, "LEFT": {"patternId": "R", "rotation": 180}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "R", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C264/initial_net.png", "targetTopFaceImage": "../images/C264/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 3, "targetRotationOffset": 270, "levelId": 264, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-264.json"}, "rollSequence": ["E", "S", "S", "N", "N", "N", "W"], "observedPathFaces": [{"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "S", "N", "N", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "E", "rotation": 180}, "RIGHT": {"patternId": "R", "rotation": 270}, "BACK": {"patternId": "R", "rotation": 270}, "LEFT": {"patternId": "R", "rotation": 180}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C264\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=R, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=R, rotation=270]\n[LEFT: patternId=R, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=R, rotation=270]\n [FRONT: patternId=E, rotation=180]\n [BOTTOM: patternId=arrow_up, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=R, rotation=270\n- LEFT: patternId=R, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=R, rotation=270\n- FRONT: patternId=E, rotation=180\n- BOTTOM: patternId=arrow_up, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C264/initial_net.png", "targetTopFaceImage": "images/C264/target_top_face.png"}, "__sample_id__": "C264"} +{"taskType": "roll_to_target_top_face", "code": "C265", "name": "Goal Roll C265", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "P", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_up", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "6", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "Q", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "Y", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "P", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_up", "rotation": 270}, "BACK": {"patternId": "6", "rotation": 0}, "LEFT": {"patternId": "Q", "rotation": 180}, "BOTTOM": {"patternId": "Y", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "Y", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C265/initial_net.png", "targetTopFaceImage": "../images/C265/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 3, "targetRotationOffset": 180, "levelId": 265, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-265.json"}, "rollSequence": ["W", "N", "W", "S", "E", "S", "E"], "observedPathFaces": [{"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "W", "S", "E", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "P", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_up", "rotation": 270}, "BACK": {"patternId": "6", "rotation": 0}, "LEFT": {"patternId": "Q", "rotation": 180}, "BOTTOM": {"patternId": "Y", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C265\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=Y, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=6, rotation=0]\n[LEFT: patternId=Q, rotation=180] [TOP: patternId=P, rotation=180] [RIGHT: patternId=arrow_up, rotation=270]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=Y, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=6, rotation=0\n- LEFT: patternId=Q, rotation=180\n- TOP: patternId=P, rotation=180\n- RIGHT: patternId=arrow_up, rotation=270\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=Y, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C265/initial_net.png", "targetTopFaceImage": "images/C265/target_top_face.png"}, "__sample_id__": "C265"} +{"taskType": "roll_to_target_top_face", "code": "C266", "name": "Goal Roll C266", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "A", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "4", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "R", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "circle", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "A", "rotation": 180}, "FRONT": {"patternId": "4", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "R", "rotation": 90}, "BOTTOM": {"patternId": "circle", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "circle", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C266/initial_net.png", "targetTopFaceImage": "../images/C266/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 2, "targetRotationOffset": 270, "levelId": 266, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-266.json"}, "rollSequence": ["W", "W", "S", "S", "N", "N"], "observedPathFaces": [{"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "S", "S", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "A", "rotation": 180}, "FRONT": {"patternId": "4", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "R", "rotation": 90}, "BOTTOM": {"patternId": "circle", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C266\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=circle, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=R, rotation=90] [TOP: patternId=A, rotation=180] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=4, rotation=0]\n [BOTTOM: patternId=circle, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=R, rotation=90\n- TOP: patternId=A, rotation=180\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=4, rotation=0\n- BOTTOM: patternId=circle, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C266/initial_net.png", "targetTopFaceImage": "images/C266/target_top_face.png"}, "__sample_id__": "C266"} +{"taskType": "roll_to_target_top_face", "code": "C267", "name": "Goal Roll C267", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "M", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "3", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Z", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "V", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "J", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "6", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "M", "rotation": 0}, "FRONT": {"patternId": "3", "rotation": 270}, "RIGHT": {"patternId": "Z", "rotation": 270}, "BACK": {"patternId": "V", "rotation": 270}, "LEFT": {"patternId": "J", "rotation": 180}, "BOTTOM": {"patternId": "6", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "6", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C267/initial_net.png", "targetTopFaceImage": "../images/C267/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 3, "targetRotationOffset": 180, "levelId": 267, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-267.json"}, "rollSequence": ["S", "W", "S", "S", "E", "S", "S"], "observedPathFaces": [{"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "S", "S", "E", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "M", "rotation": 0}, "FRONT": {"patternId": "3", "rotation": 270}, "RIGHT": {"patternId": "Z", "rotation": 270}, "BACK": {"patternId": "V", "rotation": 270}, "LEFT": {"patternId": "J", "rotation": 180}, "BOTTOM": {"patternId": "6", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C267\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=6, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=V, rotation=270]\n[LEFT: patternId=J, rotation=180] [TOP: patternId=M, rotation=0] [RIGHT: patternId=Z, rotation=270]\n [FRONT: patternId=3, rotation=270]\n [BOTTOM: patternId=6, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=V, rotation=270\n- LEFT: patternId=J, rotation=180\n- TOP: patternId=M, rotation=0\n- RIGHT: patternId=Z, rotation=270\n- FRONT: patternId=3, rotation=270\n- BOTTOM: patternId=6, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C267/initial_net.png", "targetTopFaceImage": "images/C267/target_top_face.png"}, "__sample_id__": "C267"} +{"taskType": "roll_to_target_top_face", "code": "C268", "name": "Goal Roll C268", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "arrow_down", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "diamond", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "Y", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "9", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "arrow_down", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "diamond", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 0}, "BOTTOM": {"patternId": "9", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 6, "stepNumber": 7, "patternId": "arrow_down", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C268/initial_net.png", "targetTopFaceImage": "../images/C268/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 7, "targetRotationOffset": 270, "levelId": 268, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-268.json"}, "rollSequence": ["S", "N", "N", "W", "W", "S", "S"], "observedPathFaces": [{"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "N", "N", "W", "W", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "arrow_down", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "diamond", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 0}, "BOTTOM": {"patternId": "9", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C268\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=arrow_down, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=diamond, rotation=0]\n[LEFT: patternId=Y, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=arrow_down, rotation=90]\n [BOTTOM: patternId=9, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=diamond, rotation=0\n- LEFT: patternId=Y, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=arrow_down, rotation=90\n- BOTTOM: patternId=9, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C268/initial_net.png", "targetTopFaceImage": "images/C268/target_top_face.png"}, "__sample_id__": "C268"} +{"taskType": "roll_to_target_top_face", "code": "C269", "name": "Goal Roll C269", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "C", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "Y", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_up", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "square", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_up", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "F", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "C", "rotation": 270}, "FRONT": {"patternId": "Y", "rotation": 90}, "RIGHT": {"patternId": "arrow_up", "rotation": 270}, "BACK": {"patternId": "square", "rotation": 180}, "LEFT": {"patternId": "arrow_up", "rotation": 90}, "BOTTOM": {"patternId": "F", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "F", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C269/initial_net.png", "targetTopFaceImage": "../images/C269/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 3, "targetRotationOffset": 180, "levelId": 269, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-269.json"}, "rollSequence": ["N", "W", "N", "N", "N", "W"], "observedPathFaces": [{"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "N", "N", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "C", "rotation": 270}, "FRONT": {"patternId": "Y", "rotation": 90}, "RIGHT": {"patternId": "arrow_up", "rotation": 270}, "BACK": {"patternId": "square", "rotation": 180}, "LEFT": {"patternId": "arrow_up", "rotation": 90}, "BOTTOM": {"patternId": "F", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C269\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=F, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=square, rotation=180]\n[LEFT: patternId=arrow_up, rotation=90] [TOP: patternId=C, rotation=270] [RIGHT: patternId=arrow_up, rotation=270]\n [FRONT: patternId=Y, rotation=90]\n [BOTTOM: patternId=F, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=square, rotation=180\n- LEFT: patternId=arrow_up, rotation=90\n- TOP: patternId=C, rotation=270\n- RIGHT: patternId=arrow_up, rotation=270\n- FRONT: patternId=Y, rotation=90\n- BOTTOM: patternId=F, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C269/initial_net.png", "targetTopFaceImage": "images/C269/target_top_face.png"}, "__sample_id__": "C269"} +{"taskType": "roll_to_target_top_face", "code": "C270", "name": "Goal Roll C270", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "J", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "Y", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Z", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "L", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "V", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "3", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "J", "rotation": 0}, "FRONT": {"patternId": "Y", "rotation": 180}, "RIGHT": {"patternId": "Z", "rotation": 270}, "BACK": {"patternId": "L", "rotation": 0}, "LEFT": {"patternId": "V", "rotation": 270}, "BOTTOM": {"patternId": "3", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "Y", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C270/initial_net.png", "targetTopFaceImage": "../images/C270/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 2, "targetRotationOffset": 90, "levelId": 270, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-270.json"}, "rollSequence": ["W", "N", "W", "N", "S", "W", "W"], "observedPathFaces": [{"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "W", "N", "S", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "J", "rotation": 0}, "FRONT": {"patternId": "Y", "rotation": 180}, "RIGHT": {"patternId": "Z", "rotation": 270}, "BACK": {"patternId": "L", "rotation": 0}, "LEFT": {"patternId": "V", "rotation": 270}, "BOTTOM": {"patternId": "3", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C270\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=Y, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=L, rotation=0]\n[LEFT: patternId=V, rotation=270] [TOP: patternId=J, rotation=0] [RIGHT: patternId=Z, rotation=270]\n [FRONT: patternId=Y, rotation=180]\n [BOTTOM: patternId=3, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=L, rotation=0\n- LEFT: patternId=V, rotation=270\n- TOP: patternId=J, rotation=0\n- RIGHT: patternId=Z, rotation=270\n- FRONT: patternId=Y, rotation=180\n- BOTTOM: patternId=3, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C270/initial_net.png", "targetTopFaceImage": "images/C270/target_top_face.png"}, "__sample_id__": "C270"} +{"taskType": "roll_to_target_top_face", "code": "C271", "name": "Goal Roll C271", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "heart", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "smile", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "5", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "square", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "9", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "heart", "rotation": 90}, "FRONT": {"patternId": "smile", "rotation": 270}, "RIGHT": {"patternId": "5", "rotation": 0}, "BACK": {"patternId": "square", "rotation": 90}, "LEFT": {"patternId": "9", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "square", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C271/initial_net.png", "targetTopFaceImage": "../images/C271/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 3, "targetRotationOffset": 180, "levelId": 271, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-271.json"}, "rollSequence": ["N", "N", "N", "W", "W", "S", "W"], "observedPathFaces": [{"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "N", "W", "W", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "heart", "rotation": 90}, "FRONT": {"patternId": "smile", "rotation": 270}, "RIGHT": {"patternId": "5", "rotation": 0}, "BACK": {"patternId": "square", "rotation": 90}, "LEFT": {"patternId": "9", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C271\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=square, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=square, rotation=90]\n[LEFT: patternId=9, rotation=270] [TOP: patternId=heart, rotation=90] [RIGHT: patternId=5, rotation=0]\n [FRONT: patternId=smile, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=square, rotation=90\n- LEFT: patternId=9, rotation=270\n- TOP: patternId=heart, rotation=90\n- RIGHT: patternId=5, rotation=0\n- FRONT: patternId=smile, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C271/initial_net.png", "targetTopFaceImage": "images/C271/target_top_face.png"}, "__sample_id__": "C271"} +{"taskType": "roll_to_target_top_face", "code": "C272", "name": "Goal Roll C272", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "F", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "heart", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "W", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "M", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "A", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "F", "rotation": 270}, "FRONT": {"patternId": "heart", "rotation": 0}, "RIGHT": {"patternId": "W", "rotation": 90}, "BACK": {"patternId": "M", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "A", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "heart", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C272/initial_net.png", "targetTopFaceImage": "../images/C272/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 6, "targetRotationOffset": 270, "levelId": 272, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-272.json"}, "rollSequence": ["E", "S", "W", "W", "N", "S", "W"], "observedPathFaces": [{"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "W", "W", "N", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "F", "rotation": 270}, "FRONT": {"patternId": "heart", "rotation": 0}, "RIGHT": {"patternId": "W", "rotation": 90}, "BACK": {"patternId": "M", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "A", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C272\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=heart, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=M, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=F, rotation=270] [RIGHT: patternId=W, rotation=90]\n [FRONT: patternId=heart, rotation=0]\n [BOTTOM: patternId=A, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=M, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=F, rotation=270\n- RIGHT: patternId=W, rotation=90\n- FRONT: patternId=heart, rotation=0\n- BOTTOM: patternId=A, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C272/initial_net.png", "targetTopFaceImage": "images/C272/target_top_face.png"}, "__sample_id__": "C272"} +{"taskType": "roll_to_target_top_face", "code": "C273", "name": "Goal Roll C273", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "D", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_right", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "D", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "circle", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 270}, "RIGHT": {"patternId": "arrow_right", "rotation": 0}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "circle", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "D", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C273/initial_net.png", "targetTopFaceImage": "../images/C273/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 273, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-273.json"}, "rollSequence": ["N", "E", "S", "E", "W", "N"], "observedPathFaces": [{"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "S", "E", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 270}, "RIGHT": {"patternId": "arrow_right", "rotation": 0}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "circle", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C273\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=D, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=D, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=arrow_right, rotation=0]\n [FRONT: patternId=D, rotation=270]\n [BOTTOM: patternId=circle, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=D, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=arrow_right, rotation=0\n- FRONT: patternId=D, rotation=270\n- BOTTOM: patternId=circle, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C273/initial_net.png", "targetTopFaceImage": "images/C273/target_top_face.png"}, "__sample_id__": "C273"} +{"taskType": "roll_to_target_top_face", "code": "C274", "name": "Goal Roll C274", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "arrow_left", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Y", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "9", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "B", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "7", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "arrow_left", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Y", "rotation": 90}, "BACK": {"patternId": "9", "rotation": 90}, "LEFT": {"patternId": "B", "rotation": 0}, "BOTTOM": {"patternId": "7", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "Y", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C274/initial_net.png", "targetTopFaceImage": "../images/C274/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 274, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-274.json"}, "rollSequence": ["W", "N", "W", "N", "N", "E", "N"], "observedPathFaces": [{"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "W", "N", "N", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "arrow_left", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Y", "rotation": 90}, "BACK": {"patternId": "9", "rotation": 90}, "LEFT": {"patternId": "B", "rotation": 0}, "BOTTOM": {"patternId": "7", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C274\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=Y, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=9, rotation=90]\n[LEFT: patternId=B, rotation=0] [TOP: patternId=arrow_left, rotation=0] [RIGHT: patternId=Y, rotation=90]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=7, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=9, rotation=90\n- LEFT: patternId=B, rotation=0\n- TOP: patternId=arrow_left, rotation=0\n- RIGHT: patternId=Y, rotation=90\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=7, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C274/initial_net.png", "targetTopFaceImage": "images/C274/target_top_face.png"}, "__sample_id__": "C274"} +{"taskType": "roll_to_target_top_face", "code": "C275", "name": "Goal Roll C275", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "6", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "O", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "I", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_down", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_up", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "6", "rotation": 180}, "FRONT": {"patternId": "O", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 270}, "LEFT": {"patternId": "arrow_down", "rotation": 180}, "BOTTOM": {"patternId": "arrow_up", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "6", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C275/initial_net.png", "targetTopFaceImage": "../images/C275/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 6, "targetRotationOffset": 180, "levelId": 275, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-275.json"}, "rollSequence": ["N", "N", "S", "W", "W", "S", "S"], "observedPathFaces": [{"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "S", "W", "W", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "6", "rotation": 180}, "FRONT": {"patternId": "O", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "I", "rotation": 270}, "LEFT": {"patternId": "arrow_down", "rotation": 180}, "BOTTOM": {"patternId": "arrow_up", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C275\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=6, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=I, rotation=270]\n[LEFT: patternId=arrow_down, rotation=180] [TOP: patternId=6, rotation=180] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=O, rotation=270]\n [BOTTOM: patternId=arrow_up, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=I, rotation=270\n- LEFT: patternId=arrow_down, rotation=180\n- TOP: patternId=6, rotation=180\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=O, rotation=270\n- BOTTOM: patternId=arrow_up, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C275/initial_net.png", "targetTopFaceImage": "images/C275/target_top_face.png"}, "__sample_id__": "C275"} +{"taskType": "roll_to_target_top_face", "code": "C276", "name": "Goal Roll C276", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "R", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "B", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "S", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_left", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "circle", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "R", "rotation": 180}, "FRONT": {"patternId": "B", "rotation": 270}, "RIGHT": {"patternId": "S", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "arrow_left", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C276/initial_net.png", "targetTopFaceImage": "../images/C276/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 2, "targetRotationOffset": 180, "levelId": 276, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-276.json"}, "rollSequence": ["E", "S", "E", "S", "E", "E", "E"], "observedPathFaces": [{"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "E", "S", "E", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "R", "rotation": 180}, "FRONT": {"patternId": "B", "rotation": 270}, "RIGHT": {"patternId": "S", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C276\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=arrow_left, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_left, rotation=0]\n[LEFT: patternId=circle, rotation=270] [TOP: patternId=R, rotation=180] [RIGHT: patternId=S, rotation=0]\n [FRONT: patternId=B, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_left, rotation=0\n- LEFT: patternId=circle, rotation=270\n- TOP: patternId=R, rotation=180\n- RIGHT: patternId=S, rotation=0\n- FRONT: patternId=B, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C276/initial_net.png", "targetTopFaceImage": "images/C276/target_top_face.png"}, "__sample_id__": "C276"} +{"taskType": "roll_to_target_top_face", "code": "C277", "name": "Goal Roll C277", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "arrow_up", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "7", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "R", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "2", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "arrow_up", "rotation": 270}, "FRONT": {"patternId": "7", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "R", "rotation": 90}, "LEFT": {"patternId": "2", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "R", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C277/initial_net.png", "targetTopFaceImage": "../images/C277/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 277, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-277.json"}, "rollSequence": ["S", "W", "S", "E", "N", "W", "N"], "observedPathFaces": [{"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "S", "E", "N", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "arrow_up", "rotation": 270}, "FRONT": {"patternId": "7", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "R", "rotation": 90}, "LEFT": {"patternId": "2", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C277\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=R, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=R, rotation=90]\n[LEFT: patternId=2, rotation=270] [TOP: patternId=arrow_up, rotation=270] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=7, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=R, rotation=90\n- LEFT: patternId=2, rotation=270\n- TOP: patternId=arrow_up, rotation=270\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=7, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C277/initial_net.png", "targetTopFaceImage": "images/C277/target_top_face.png"}, "__sample_id__": "C277"} +{"taskType": "roll_to_target_top_face", "code": "C278", "name": "Goal Roll C278", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "B", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "D", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "A", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "6", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "B", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "D", "rotation": 270}, "LEFT": {"patternId": "A", "rotation": 180}, "BOTTOM": {"patternId": "6", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "6", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C278/initial_net.png", "targetTopFaceImage": "../images/C278/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 6, "targetRotationOffset": 90, "levelId": 278, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-278.json"}, "rollSequence": ["W", "E", "N", "S", "N", "N"], "observedPathFaces": [{"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "E", "N", "S", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "B", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "D", "rotation": 270}, "LEFT": {"patternId": "A", "rotation": 180}, "BOTTOM": {"patternId": "6", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C278\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=6, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=D, rotation=270]\n[LEFT: patternId=A, rotation=180] [TOP: patternId=B, rotation=270] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=6, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=D, rotation=270\n- LEFT: patternId=A, rotation=180\n- TOP: patternId=B, rotation=270\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=6, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C278/initial_net.png", "targetTopFaceImage": "images/C278/target_top_face.png"}, "__sample_id__": "C278"} +{"taskType": "roll_to_target_top_face", "code": "C279", "name": "Goal Roll C279", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "O", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "N", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_up", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "2", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "O", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 270}, "RIGHT": {"patternId": "arrow_up", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "2", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "arrow_up", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C279/initial_net.png", "targetTopFaceImage": "../images/C279/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 279, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-279.json"}, "rollSequence": ["W", "S", "W", "E", "W", "S"], "observedPathFaces": [{"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "W", "E", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 270}, "RIGHT": {"patternId": "arrow_up", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "2", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C279\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=arrow_up, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=2, rotation=180] [TOP: patternId=O, rotation=0] [RIGHT: patternId=arrow_up, rotation=180]\n [FRONT: patternId=N, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=2, rotation=180\n- TOP: patternId=O, rotation=0\n- RIGHT: patternId=arrow_up, rotation=180\n- FRONT: patternId=N, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C279/initial_net.png", "targetTopFaceImage": "images/C279/target_top_face.png"}, "__sample_id__": "C279"} +{"taskType": "roll_to_target_top_face", "code": "C280", "name": "Goal Roll C280", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "D", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "5", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "C", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "H", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_up", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "U", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "D", "rotation": 270}, "FRONT": {"patternId": "5", "rotation": 180}, "RIGHT": {"patternId": "C", "rotation": 90}, "BACK": {"patternId": "H", "rotation": 180}, "LEFT": {"patternId": "arrow_up", "rotation": 90}, "BOTTOM": {"patternId": "U", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "5", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C280/initial_net.png", "targetTopFaceImage": "../images/C280/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 2, "targetRotationOffset": 90, "levelId": 280, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-280.json"}, "rollSequence": ["W", "N", "N", "N", "E", "S", "S"], "observedPathFaces": [{"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "N", "N", "E", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "D", "rotation": 270}, "FRONT": {"patternId": "5", "rotation": 180}, "RIGHT": {"patternId": "C", "rotation": 90}, "BACK": {"patternId": "H", "rotation": 180}, "LEFT": {"patternId": "arrow_up", "rotation": 90}, "BOTTOM": {"patternId": "U", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C280\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=5, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=H, rotation=180]\n[LEFT: patternId=arrow_up, rotation=90] [TOP: patternId=D, rotation=270] [RIGHT: patternId=C, rotation=90]\n [FRONT: patternId=5, rotation=180]\n [BOTTOM: patternId=U, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=H, rotation=180\n- LEFT: patternId=arrow_up, rotation=90\n- TOP: patternId=D, rotation=270\n- RIGHT: patternId=C, rotation=90\n- FRONT: patternId=5, rotation=180\n- BOTTOM: patternId=U, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C280/initial_net.png", "targetTopFaceImage": "images/C280/target_top_face.png"}, "__sample_id__": "C280"} +{"taskType": "roll_to_target_top_face", "code": "C281", "name": "Goal Roll C281", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "arrow_right", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "J", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "diamond", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "C", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_left", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "arrow_right", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "J", "rotation": 180}, "BACK": {"patternId": "diamond", "rotation": 270}, "LEFT": {"patternId": "C", "rotation": 270}, "BOTTOM": {"patternId": "arrow_left", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "J", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C281/initial_net.png", "targetTopFaceImage": "../images/C281/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 281, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-281.json"}, "rollSequence": ["W", "W", "W", "E", "E", "E", "N"], "observedPathFaces": [{"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "W", "E", "E", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "arrow_right", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "J", "rotation": 180}, "BACK": {"patternId": "diamond", "rotation": 270}, "LEFT": {"patternId": "C", "rotation": 270}, "BOTTOM": {"patternId": "arrow_left", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C281\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=J, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=diamond, rotation=270]\n[LEFT: patternId=C, rotation=270] [TOP: patternId=arrow_right, rotation=90] [RIGHT: patternId=J, rotation=180]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=arrow_left, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=diamond, rotation=270\n- LEFT: patternId=C, rotation=270\n- TOP: patternId=arrow_right, rotation=90\n- RIGHT: patternId=J, rotation=180\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=arrow_left, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C281/initial_net.png", "targetTopFaceImage": "images/C281/target_top_face.png"}, "__sample_id__": "C281"} +{"taskType": "roll_to_target_top_face", "code": "C282", "name": "Goal Roll C282", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "7", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "H", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "4", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "Z", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "7", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "7", "rotation": 90}, "FRONT": {"patternId": "H", "rotation": 90}, "RIGHT": {"patternId": "4", "rotation": 0}, "BACK": {"patternId": "Z", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "7", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "Z", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C282/initial_net.png", "targetTopFaceImage": "../images/C282/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 282, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-282.json"}, "rollSequence": ["S", "S", "E", "S", "E", "E", "E"], "observedPathFaces": [{"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "E", "S", "E", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "7", "rotation": 90}, "FRONT": {"patternId": "H", "rotation": 90}, "RIGHT": {"patternId": "4", "rotation": 0}, "BACK": {"patternId": "Z", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "7", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C282\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=Z, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=Z, rotation=270]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=7, rotation=90] [RIGHT: patternId=4, rotation=0]\n [FRONT: patternId=H, rotation=90]\n [BOTTOM: patternId=7, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Z, rotation=270\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=7, rotation=90\n- RIGHT: patternId=4, rotation=0\n- FRONT: patternId=H, rotation=90\n- BOTTOM: patternId=7, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C282/initial_net.png", "targetTopFaceImage": "images/C282/target_top_face.png"}, "__sample_id__": "C282"} +{"taskType": "roll_to_target_top_face", "code": "C283", "name": "Goal Roll C283", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "Z", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "triangle", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "A", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "1", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "Z", "rotation": 90}, "RIGHT": {"patternId": "triangle", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "A", "rotation": 0}, "BOTTOM": {"patternId": "1", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "triangle", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C283/initial_net.png", "targetTopFaceImage": "../images/C283/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 6, "targetRotationOffset": 90, "levelId": 283, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-283.json"}, "rollSequence": ["E", "S", "S", "W", "N", "E"], "observedPathFaces": [{"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "S", "W", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "Z", "rotation": 90}, "RIGHT": {"patternId": "triangle", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "A", "rotation": 0}, "BOTTOM": {"patternId": "1", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C283\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=triangle, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=A, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=triangle, rotation=270]\n [FRONT: patternId=Z, rotation=90]\n [BOTTOM: patternId=1, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=A, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=triangle, rotation=270\n- FRONT: patternId=Z, rotation=90\n- BOTTOM: patternId=1, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C283/initial_net.png", "targetTopFaceImage": "images/C283/target_top_face.png"}, "__sample_id__": "C283"} +{"taskType": "roll_to_target_top_face", "code": "C284", "name": "Goal Roll C284", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "S", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Z", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "B", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "4", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "heart", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "S", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Z", "rotation": 270}, "BACK": {"patternId": "B", "rotation": 90}, "LEFT": {"patternId": "4", "rotation": 270}, "BOTTOM": {"patternId": "heart", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "heart", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C284/initial_net.png", "targetTopFaceImage": "../images/C284/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 6, "targetRotationOffset": 180, "levelId": 284, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-284.json"}, "rollSequence": ["W", "W", "N", "N", "W", "W"], "observedPathFaces": [{"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "N", "N", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "S", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "Z", "rotation": 270}, "BACK": {"patternId": "B", "rotation": 90}, "LEFT": {"patternId": "4", "rotation": 270}, "BOTTOM": {"patternId": "heart", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C284\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=heart, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=B, rotation=90]\n[LEFT: patternId=4, rotation=270] [TOP: patternId=S, rotation=180] [RIGHT: patternId=Z, rotation=270]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=heart, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=B, rotation=90\n- LEFT: patternId=4, rotation=270\n- TOP: patternId=S, rotation=180\n- RIGHT: patternId=Z, rotation=270\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=heart, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C284/initial_net.png", "targetTopFaceImage": "images/C284/target_top_face.png"}, "__sample_id__": "C284"} +{"taskType": "roll_to_target_top_face", "code": "C285", "name": "Goal Roll C285", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "diamond", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "6", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "S", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "O", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "diamond", "rotation": 270}, "FRONT": {"patternId": "6", "rotation": 90}, "RIGHT": {"patternId": "S", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "O", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "S", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C285/initial_net.png", "targetTopFaceImage": "../images/C285/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 285, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-285.json"}, "rollSequence": ["W", "S", "W", "E", "S", "W", "N"], "observedPathFaces": [{"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "W", "E", "S", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "diamond", "rotation": 270}, "FRONT": {"patternId": "6", "rotation": 90}, "RIGHT": {"patternId": "S", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "O", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C285\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=S, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=O, rotation=0] [TOP: patternId=diamond, rotation=270] [RIGHT: patternId=S, rotation=90]\n [FRONT: patternId=6, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=O, rotation=0\n- TOP: patternId=diamond, rotation=270\n- RIGHT: patternId=S, rotation=90\n- FRONT: patternId=6, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C285/initial_net.png", "targetTopFaceImage": "images/C285/target_top_face.png"}, "__sample_id__": "C285"} +{"taskType": "roll_to_target_top_face", "code": "C286", "name": "Goal Roll C286", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "circle", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "smile", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "O", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "3", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "circle", "rotation": 90}, "FRONT": {"patternId": "smile", "rotation": 270}, "RIGHT": {"patternId": "O", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "3", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C286/initial_net.png", "targetTopFaceImage": "../images/C286/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 6, "targetRotationOffset": 180, "levelId": 286, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-286.json"}, "rollSequence": ["W", "S", "W", "N", "E", "E"], "observedPathFaces": [{"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "W", "N", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "circle", "rotation": 90}, "FRONT": {"patternId": "smile", "rotation": 270}, "RIGHT": {"patternId": "O", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C286\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=3, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=3, rotation=0] [TOP: patternId=circle, rotation=90] [RIGHT: patternId=O, rotation=180]\n [FRONT: patternId=smile, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=3, rotation=0\n- TOP: patternId=circle, rotation=90\n- RIGHT: patternId=O, rotation=180\n- FRONT: patternId=smile, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C286/initial_net.png", "targetTopFaceImage": "images/C286/target_top_face.png"}, "__sample_id__": "C286"} +{"taskType": "roll_to_target_top_face", "code": "C287", "name": "Goal Roll C287", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "K", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "D", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_left", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "I", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "K", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "D", "rotation": 270}, "BACK": {"patternId": "arrow_left", "rotation": 90}, "LEFT": {"patternId": "I", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "I", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C287/initial_net.png", "targetTopFaceImage": "../images/C287/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 5, "targetRotationOffset": 90, "levelId": 287, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-287.json"}, "rollSequence": ["W", "N", "W", "E", "N", "W"], "observedPathFaces": [{"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "W", "E", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "K", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "D", "rotation": 270}, "BACK": {"patternId": "arrow_left", "rotation": 90}, "LEFT": {"patternId": "I", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C287\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=I, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_left, rotation=90]\n[LEFT: patternId=I, rotation=270] [TOP: patternId=K, rotation=270] [RIGHT: patternId=D, rotation=270]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_left, rotation=90\n- LEFT: patternId=I, rotation=270\n- TOP: patternId=K, rotation=270\n- RIGHT: patternId=D, rotation=270\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C287/initial_net.png", "targetTopFaceImage": "images/C287/target_top_face.png"}, "__sample_id__": "C287"} +{"taskType": "roll_to_target_top_face", "code": "C288", "name": "Goal Roll C288", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "plus", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "9", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "R", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "9", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "plus", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "9", "rotation": 0}, "LEFT": {"patternId": "R", "rotation": 0}, "BOTTOM": {"patternId": "9", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "plus", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C288/initial_net.png", "targetTopFaceImage": "../images/C288/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 4, "targetRotationOffset": 90, "levelId": 288, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-288.json"}, "rollSequence": ["W", "S", "E", "E", "N", "N"], "observedPathFaces": [{"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "E", "E", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "plus", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "9", "rotation": 0}, "LEFT": {"patternId": "R", "rotation": 0}, "BOTTOM": {"patternId": "9", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C288\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=plus, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=9, rotation=0]\n[LEFT: patternId=R, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=plus, rotation=180]\n [BOTTOM: patternId=9, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=9, rotation=0\n- LEFT: patternId=R, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=plus, rotation=180\n- BOTTOM: patternId=9, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C288/initial_net.png", "targetTopFaceImage": "images/C288/target_top_face.png"}, "__sample_id__": "C288"} +{"taskType": "roll_to_target_top_face", "code": "C289", "name": "Goal Roll C289", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "E", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "M", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "Q", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_up", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "E", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "Q", "rotation": 180}, "BOTTOM": {"patternId": "arrow_up", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "E", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C289/initial_net.png", "targetTopFaceImage": "../images/C289/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 5, "targetRotationOffset": 270, "levelId": 289, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-289.json"}, "rollSequence": ["N", "W", "N", "E", "E", "W"], "observedPathFaces": [{"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "N", "E", "E", "W"]}, "legacy_answer": {"TOP": {"patternId": "E", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "Q", "rotation": 180}, "BOTTOM": {"patternId": "arrow_up", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C289\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=E, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=M, rotation=0]\n[LEFT: patternId=Q, rotation=180] [TOP: patternId=E, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=arrow_up, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=M, rotation=0\n- LEFT: patternId=Q, rotation=180\n- TOP: patternId=E, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=arrow_up, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C289/initial_net.png", "targetTopFaceImage": "images/C289/target_top_face.png"}, "__sample_id__": "C289"} +{"taskType": "roll_to_target_top_face", "code": "C290", "name": "Goal Roll C290", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "arrow_up", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "J", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "K", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "P", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "J", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "arrow_up", "rotation": 0}, "FRONT": {"patternId": "J", "rotation": 90}, "RIGHT": {"patternId": "K", "rotation": 0}, "BACK": {"patternId": "P", "rotation": 90}, "LEFT": {"patternId": "J", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "P", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C290/initial_net.png", "targetTopFaceImage": "../images/C290/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 290, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-290.json"}, "rollSequence": ["S", "S", "E", "S", "S", "S"], "observedPathFaces": [{"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "E", "S", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "arrow_up", "rotation": 0}, "FRONT": {"patternId": "J", "rotation": 90}, "RIGHT": {"patternId": "K", "rotation": 0}, "BACK": {"patternId": "P", "rotation": 90}, "LEFT": {"patternId": "J", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C290\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=P, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=P, rotation=90]\n[LEFT: patternId=J, rotation=270] [TOP: patternId=arrow_up, rotation=0] [RIGHT: patternId=K, rotation=0]\n [FRONT: patternId=J, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=P, rotation=90\n- LEFT: patternId=J, rotation=270\n- TOP: patternId=arrow_up, rotation=0\n- RIGHT: patternId=K, rotation=0\n- FRONT: patternId=J, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C290/initial_net.png", "targetTopFaceImage": "images/C290/target_top_face.png"}, "__sample_id__": "C290"} +{"taskType": "roll_to_target_top_face", "code": "C291", "name": "Goal Roll C291", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "6", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "J", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "G", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "plus", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "C", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "star", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "6", "rotation": 90}, "FRONT": {"patternId": "J", "rotation": 90}, "RIGHT": {"patternId": "G", "rotation": 180}, "BACK": {"patternId": "plus", "rotation": 90}, "LEFT": {"patternId": "C", "rotation": 0}, "BOTTOM": {"patternId": "star", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "6", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C291/initial_net.png", "targetTopFaceImage": "../images/C291/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 5, "targetRotationOffset": 270, "levelId": 291, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-291.json"}, "rollSequence": ["S", "W", "S", "S", "S", "W"], "observedPathFaces": [{"patternId": "J", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "S", "S", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "6", "rotation": 90}, "FRONT": {"patternId": "J", "rotation": 90}, "RIGHT": {"patternId": "G", "rotation": 180}, "BACK": {"patternId": "plus", "rotation": 90}, "LEFT": {"patternId": "C", "rotation": 0}, "BOTTOM": {"patternId": "star", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C291\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=6, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=plus, rotation=90]\n[LEFT: patternId=C, rotation=0] [TOP: patternId=6, rotation=90] [RIGHT: patternId=G, rotation=180]\n [FRONT: patternId=J, rotation=90]\n [BOTTOM: patternId=star, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=plus, rotation=90\n- LEFT: patternId=C, rotation=0\n- TOP: patternId=6, rotation=90\n- RIGHT: patternId=G, rotation=180\n- FRONT: patternId=J, rotation=90\n- BOTTOM: patternId=star, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C291/initial_net.png", "targetTopFaceImage": "images/C291/target_top_face.png"}, "__sample_id__": "C291"} +{"taskType": "roll_to_target_top_face", "code": "C292", "name": "Goal Roll C292", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "K", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "I", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "S", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "7", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "K", "rotation": 180}, "FRONT": {"patternId": "I", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "7", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "S", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C292/initial_net.png", "targetTopFaceImage": "../images/C292/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 292, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-292.json"}, "rollSequence": ["W", "W", "S", "W", "N", "N", "E"], "observedPathFaces": [{"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "S", "W", "N", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "K", "rotation": 180}, "FRONT": {"patternId": "I", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "7", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C292\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=S, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=7, rotation=0] [TOP: patternId=K, rotation=180] [RIGHT: patternId=S, rotation=270]\n [FRONT: patternId=I, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=7, rotation=0\n- TOP: patternId=K, rotation=180\n- RIGHT: patternId=S, rotation=270\n- FRONT: patternId=I, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C292/initial_net.png", "targetTopFaceImage": "images/C292/target_top_face.png"}, "__sample_id__": "C292"} +{"taskType": "roll_to_target_top_face", "code": "C293", "name": "Goal Roll C293", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "D", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "K", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "D", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "5", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "7", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "D", "rotation": 180}, "FRONT": {"patternId": "K", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "D", "rotation": 270}, "LEFT": {"patternId": "5", "rotation": 0}, "BOTTOM": {"patternId": "7", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "K", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C293/initial_net.png", "targetTopFaceImage": "../images/C293/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 4, "targetRotationOffset": 270, "levelId": 293, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-293.json"}, "rollSequence": ["W", "S", "E", "E", "N", "E"], "observedPathFaces": [{"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "E", "E", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "D", "rotation": 180}, "FRONT": {"patternId": "K", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "D", "rotation": 270}, "LEFT": {"patternId": "5", "rotation": 0}, "BOTTOM": {"patternId": "7", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C293\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=K, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=D, rotation=270]\n[LEFT: patternId=5, rotation=0] [TOP: patternId=D, rotation=180] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=K, rotation=0]\n [BOTTOM: patternId=7, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=D, rotation=270\n- LEFT: patternId=5, rotation=0\n- TOP: patternId=D, rotation=180\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=K, rotation=0\n- BOTTOM: patternId=7, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C293/initial_net.png", "targetTopFaceImage": "images/C293/target_top_face.png"}, "__sample_id__": "C293"} +{"taskType": "roll_to_target_top_face", "code": "C294", "name": "Goal Roll C294", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "P", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "Q", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "4", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "3", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "3", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "P", "rotation": 270}, "FRONT": {"patternId": "Q", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "4", "rotation": 270}, "LEFT": {"patternId": "3", "rotation": 90}, "BOTTOM": {"patternId": "3", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 6, "stepNumber": 7, "patternId": "4", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C294/initial_net.png", "targetTopFaceImage": "../images/C294/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 7, "targetRotationOffset": 90, "levelId": 294, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-294.json"}, "rollSequence": ["W", "N", "E", "S", "E", "S", "N"], "observedPathFaces": [{"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "E", "S", "E", "S", "N"]}, "legacy_answer": {"TOP": {"patternId": "P", "rotation": 270}, "FRONT": {"patternId": "Q", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "4", "rotation": 270}, "LEFT": {"patternId": "3", "rotation": 90}, "BOTTOM": {"patternId": "3", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C294\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=4, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=4, rotation=270]\n[LEFT: patternId=3, rotation=90] [TOP: patternId=P, rotation=270] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=Q, rotation=90]\n [BOTTOM: patternId=3, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=4, rotation=270\n- LEFT: patternId=3, rotation=90\n- TOP: patternId=P, rotation=270\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=Q, rotation=90\n- BOTTOM: patternId=3, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C294/initial_net.png", "targetTopFaceImage": "images/C294/target_top_face.png"}, "__sample_id__": "C294"} +{"taskType": "roll_to_target_top_face", "code": "C295", "name": "Goal Roll C295", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "2", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "K", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "C", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "O", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "Q", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "2", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "K", "rotation": 270}, "BACK": {"patternId": "C", "rotation": 180}, "LEFT": {"patternId": "O", "rotation": 270}, "BOTTOM": {"patternId": "Q", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "2", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C295/initial_net.png", "targetTopFaceImage": "../images/C295/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 5, "targetRotationOffset": 180, "levelId": 295, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-295.json"}, "rollSequence": ["E", "W", "N", "W", "S", "S", "S"], "observedPathFaces": [{"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "W", "N", "W", "S", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "2", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "K", "rotation": 270}, "BACK": {"patternId": "C", "rotation": 180}, "LEFT": {"patternId": "O", "rotation": 270}, "BOTTOM": {"patternId": "Q", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C295\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=2, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=C, rotation=180]\n[LEFT: patternId=O, rotation=270] [TOP: patternId=2, rotation=0] [RIGHT: patternId=K, rotation=270]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=Q, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=C, rotation=180\n- LEFT: patternId=O, rotation=270\n- TOP: patternId=2, rotation=0\n- RIGHT: patternId=K, rotation=270\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=Q, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C295/initial_net.png", "targetTopFaceImage": "images/C295/target_top_face.png"}, "__sample_id__": "C295"} +{"taskType": "roll_to_target_top_face", "code": "C296", "name": "Goal Roll C296", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "R", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "7", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "D", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "3", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "M", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "R", "rotation": 90}, "FRONT": {"patternId": "7", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 180}, "BOTTOM": {"patternId": "M", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "R", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C296/initial_net.png", "targetTopFaceImage": "../images/C296/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 5, "targetRotationOffset": 270, "levelId": 296, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-296.json"}, "rollSequence": ["S", "W", "S", "W", "W", "N", "S"], "observedPathFaces": [{"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "S", "W", "W", "N", "S"]}, "legacy_answer": {"TOP": {"patternId": "R", "rotation": 90}, "FRONT": {"patternId": "7", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 180}, "BOTTOM": {"patternId": "M", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C296\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=R, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=D, rotation=0]\n[LEFT: patternId=3, rotation=180] [TOP: patternId=R, rotation=90] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=7, rotation=90]\n [BOTTOM: patternId=M, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=D, rotation=0\n- LEFT: patternId=3, rotation=180\n- TOP: patternId=R, rotation=90\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=7, rotation=90\n- BOTTOM: patternId=M, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C296/initial_net.png", "targetTopFaceImage": "images/C296/target_top_face.png"}, "__sample_id__": "C296"} +{"taskType": "roll_to_target_top_face", "code": "C297", "name": "Goal Roll C297", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "C", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "M", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "6", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "8", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "C", "rotation": 270}, "RIGHT": {"patternId": "M", "rotation": 270}, "BACK": {"patternId": "6", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "6", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C297/initial_net.png", "targetTopFaceImage": "../images/C297/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 3, "targetRotationOffset": 90, "levelId": 297, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-297.json"}, "rollSequence": ["N", "W", "W", "E", "E", "E"], "observedPathFaces": [{"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "W", "E", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "C", "rotation": 270}, "RIGHT": {"patternId": "M", "rotation": 270}, "BACK": {"patternId": "6", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C297\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=6, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=6, rotation=0]\n[LEFT: patternId=8, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=M, rotation=270]\n [FRONT: patternId=C, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=6, rotation=0\n- LEFT: patternId=8, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=M, rotation=270\n- FRONT: patternId=C, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C297/initial_net.png", "targetTopFaceImage": "images/C297/target_top_face.png"}, "__sample_id__": "C297"} +{"taskType": "roll_to_target_top_face", "code": "C298", "name": "Goal Roll C298", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "M", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "T", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "5", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "M", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "I", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "M", "rotation": 180}, "RIGHT": {"patternId": "T", "rotation": 270}, "BACK": {"patternId": "5", "rotation": 180}, "LEFT": {"patternId": "M", "rotation": 90}, "BOTTOM": {"patternId": "I", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "T", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C298/initial_net.png", "targetTopFaceImage": "../images/C298/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 2, "targetRotationOffset": 180, "levelId": 298, "moveCount": 6, "sourceLevelPath": "levels/reconstruct/generated-298.json"}, "rollSequence": ["S", "W", "W", "W", "N", "W"], "observedPathFaces": [{"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "W", "W", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "M", "rotation": 180}, "RIGHT": {"patternId": "T", "rotation": 270}, "BACK": {"patternId": "5", "rotation": 180}, "LEFT": {"patternId": "M", "rotation": 90}, "BOTTOM": {"patternId": "I", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C298\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=T, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=5, rotation=180]\n[LEFT: patternId=M, rotation=90] [TOP: patternId=?, rotation=0] [RIGHT: patternId=T, rotation=270]\n [FRONT: patternId=M, rotation=180]\n [BOTTOM: patternId=I, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=5, rotation=180\n- LEFT: patternId=M, rotation=90\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=T, rotation=270\n- FRONT: patternId=M, rotation=180\n- BOTTOM: patternId=I, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C298/initial_net.png", "targetTopFaceImage": "images/C298/target_top_face.png"}, "__sample_id__": "C298"} +{"taskType": "roll_to_target_top_face", "code": "C299", "name": "Goal Roll C299", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "Y", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "G", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "C", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "G", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "T", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "Y", "rotation": 90}, "RIGHT": {"patternId": "G", "rotation": 180}, "BACK": {"patternId": "C", "rotation": 90}, "LEFT": {"patternId": "G", "rotation": 180}, "BOTTOM": {"patternId": "T", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "G", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C299/initial_net.png", "targetTopFaceImage": "../images/C299/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 4, "targetRotationOffset": 180, "levelId": 299, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-299.json"}, "rollSequence": ["S", "E", "N", "S", "E", "E", "E"], "observedPathFaces": [{"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "N", "S", "E", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "Y", "rotation": 90}, "RIGHT": {"patternId": "G", "rotation": 180}, "BACK": {"patternId": "C", "rotation": 90}, "LEFT": {"patternId": "G", "rotation": 180}, "BOTTOM": {"patternId": "T", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C299\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=G, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=C, rotation=90]\n[LEFT: patternId=G, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=G, rotation=180]\n [FRONT: patternId=Y, rotation=90]\n [BOTTOM: patternId=T, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=C, rotation=90\n- LEFT: patternId=G, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=G, rotation=180\n- FRONT: patternId=Y, rotation=90\n- BOTTOM: patternId=T, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C299/initial_net.png", "targetTopFaceImage": "images/C299/target_top_face.png"}, "__sample_id__": "C299"} +{"taskType": "roll_to_target_top_face", "code": "C300", "name": "Goal Roll C300", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "N", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "Q", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "5", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "R", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "5", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "S", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "N", "rotation": 90}, "FRONT": {"patternId": "Q", "rotation": 0}, "RIGHT": {"patternId": "5", "rotation": 0}, "BACK": {"patternId": "R", "rotation": 90}, "LEFT": {"patternId": "5", "rotation": 180}, "BOTTOM": {"patternId": "S", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "R", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C300/initial_net.png", "targetTopFaceImage": "../images/C300/target_top_face.png"}, "metadata": {"difficulty": 3, "tier": 3, "targetStepNumber": 5, "targetRotationOffset": 270, "levelId": 300, "moveCount": 7, "sourceLevelPath": "levels/reconstruct/generated-300.json"}, "rollSequence": ["N", "N", "W", "E", "N", "E", "N"], "observedPathFaces": [{"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "W", "E", "N", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "N", "rotation": 90}, "FRONT": {"patternId": "Q", "rotation": 0}, "RIGHT": {"patternId": "5", "rotation": 0}, "BACK": {"patternId": "R", "rotation": 90}, "LEFT": {"patternId": "5", "rotation": 180}, "BOTTOM": {"patternId": "S", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C300\n- task_type: roll_to_target_top_face\n- difficulty: 3\n- target_top_face: patternId=R, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=R, rotation=90]\n[LEFT: patternId=5, rotation=180] [TOP: patternId=N, rotation=90] [RIGHT: patternId=5, rotation=0]\n [FRONT: patternId=Q, rotation=0]\n [BOTTOM: patternId=S, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=R, rotation=90\n- LEFT: patternId=5, rotation=180\n- TOP: patternId=N, rotation=90\n- RIGHT: patternId=5, rotation=0\n- FRONT: patternId=Q, rotation=0\n- BOTTOM: patternId=S, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C300/initial_net.png", "targetTopFaceImage": "images/C300/target_top_face.png"}, "__sample_id__": "C300"} +{"taskType": "roll_to_target_top_face", "code": "C301", "name": "Goal Roll C301", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "arrow_down", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "arrow_up", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "2", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_left", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "P", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "arrow_down", "rotation": 0}, "FRONT": {"patternId": "arrow_up", "rotation": 270}, "RIGHT": {"patternId": "2", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_left", "rotation": 0}, "BOTTOM": {"patternId": "P", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "2", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C301/initial_net.png", "targetTopFaceImage": "../images/C301/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 3, "targetRotationOffset": 90, "levelId": 301, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-301.json"}, "rollSequence": ["E", "W", "W", "W", "E", "S", "S", "N", "E"], "observedPathFaces": [{"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "W", "W", "W", "E", "S", "S", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "arrow_down", "rotation": 0}, "FRONT": {"patternId": "arrow_up", "rotation": 270}, "RIGHT": {"patternId": "2", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_left", "rotation": 0}, "BOTTOM": {"patternId": "P", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C301\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=2, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=arrow_left, rotation=0] [TOP: patternId=arrow_down, rotation=0] [RIGHT: patternId=2, rotation=270]\n [FRONT: patternId=arrow_up, rotation=270]\n [BOTTOM: patternId=P, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=arrow_left, rotation=0\n- TOP: patternId=arrow_down, rotation=0\n- RIGHT: patternId=2, rotation=270\n- FRONT: patternId=arrow_up, rotation=270\n- BOTTOM: patternId=P, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C301/initial_net.png", "targetTopFaceImage": "images/C301/target_top_face.png"}, "__sample_id__": "C301"} +{"taskType": "roll_to_target_top_face", "code": "C302", "name": "Goal Roll C302", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "3", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "V", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "1", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "diamond", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "E", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "3", "rotation": 0}, "FRONT": {"patternId": "V", "rotation": 90}, "RIGHT": {"patternId": "1", "rotation": 90}, "BACK": {"patternId": "diamond", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "E", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 6, "stepNumber": 7, "patternId": "diamond", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C302/initial_net.png", "targetTopFaceImage": "../images/C302/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 7, "targetRotationOffset": 90, "levelId": 302, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-302.json"}, "rollSequence": ["N", "E", "S", "W", "W", "N", "W", "S"], "observedPathFaces": [{"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "S", "W", "W", "N", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "3", "rotation": 0}, "FRONT": {"patternId": "V", "rotation": 90}, "RIGHT": {"patternId": "1", "rotation": 90}, "BACK": {"patternId": "diamond", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "E", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C302\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=diamond, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=diamond, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=3, rotation=0] [RIGHT: patternId=1, rotation=90]\n [FRONT: patternId=V, rotation=90]\n [BOTTOM: patternId=E, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=diamond, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=3, rotation=0\n- RIGHT: patternId=1, rotation=90\n- FRONT: patternId=V, rotation=90\n- BOTTOM: patternId=E, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C302/initial_net.png", "targetTopFaceImage": "images/C302/target_top_face.png"}, "__sample_id__": "C302"} +{"taskType": "roll_to_target_top_face", "code": "C303", "name": "Goal Roll C303", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "I", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "X", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "plus", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "9", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "triangle", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "I", "rotation": 270}, "RIGHT": {"patternId": "X", "rotation": 0}, "BACK": {"patternId": "plus", "rotation": 270}, "LEFT": {"patternId": "9", "rotation": 90}, "BOTTOM": {"patternId": "triangle", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "plus", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C303/initial_net.png", "targetTopFaceImage": "../images/C303/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 2, "targetRotationOffset": 90, "levelId": 303, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-303.json"}, "rollSequence": ["W", "S", "S", "S", "E", "S", "E", "N", "E"], "observedPathFaces": [{"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "S", "S", "E", "S", "E", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "I", "rotation": 270}, "RIGHT": {"patternId": "X", "rotation": 0}, "BACK": {"patternId": "plus", "rotation": 270}, "LEFT": {"patternId": "9", "rotation": 90}, "BOTTOM": {"patternId": "triangle", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C303\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=plus, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=plus, rotation=270]\n[LEFT: patternId=9, rotation=90] [TOP: patternId=?, rotation=0] [RIGHT: patternId=X, rotation=0]\n [FRONT: patternId=I, rotation=270]\n [BOTTOM: patternId=triangle, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=plus, rotation=270\n- LEFT: patternId=9, rotation=90\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=X, rotation=0\n- FRONT: patternId=I, rotation=270\n- BOTTOM: patternId=triangle, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C303/initial_net.png", "targetTopFaceImage": "images/C303/target_top_face.png"}, "__sample_id__": "C303"} +{"taskType": "roll_to_target_top_face", "code": "C304", "name": "Goal Roll C304", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "2", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "R", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_left", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "8", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "E", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "2", "rotation": 90}, "FRONT": {"patternId": "R", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 180}, "LEFT": {"patternId": "8", "rotation": 90}, "BOTTOM": {"patternId": "E", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "R", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C304/initial_net.png", "targetTopFaceImage": "../images/C304/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 5, "targetRotationOffset": 90, "levelId": 304, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-304.json"}, "rollSequence": ["W", "S", "N", "E", "N", "S", "W", "W"], "observedPathFaces": [{"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "N", "E", "N", "S", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "2", "rotation": 90}, "FRONT": {"patternId": "R", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 180}, "LEFT": {"patternId": "8", "rotation": 90}, "BOTTOM": {"patternId": "E", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C304\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=R, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_left, rotation=180]\n[LEFT: patternId=8, rotation=90] [TOP: patternId=2, rotation=90] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=R, rotation=270]\n [BOTTOM: patternId=E, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_left, rotation=180\n- LEFT: patternId=8, rotation=90\n- TOP: patternId=2, rotation=90\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=R, rotation=270\n- BOTTOM: patternId=E, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C304/initial_net.png", "targetTopFaceImage": "images/C304/target_top_face.png"}, "__sample_id__": "C304"} +{"taskType": "roll_to_target_top_face", "code": "C305", "name": "Goal Roll C305", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "8", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "triangle", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Q", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "I", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "Y", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "8", "rotation": 90}, "FRONT": {"patternId": "triangle", "rotation": 180}, "RIGHT": {"patternId": "Q", "rotation": 90}, "BACK": {"patternId": "I", "rotation": 270}, "LEFT": {"patternId": "Y", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "Y", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C305/initial_net.png", "targetTopFaceImage": "../images/C305/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 305, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-305.json"}, "rollSequence": ["E", "N", "E", "E", "S", "W", "S", "W"], "observedPathFaces": [{"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "E", "E", "S", "W", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "8", "rotation": 90}, "FRONT": {"patternId": "triangle", "rotation": 180}, "RIGHT": {"patternId": "Q", "rotation": 90}, "BACK": {"patternId": "I", "rotation": 270}, "LEFT": {"patternId": "Y", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C305\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=Y, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=I, rotation=270]\n[LEFT: patternId=Y, rotation=0] [TOP: patternId=8, rotation=90] [RIGHT: patternId=Q, rotation=90]\n [FRONT: patternId=triangle, rotation=180]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=I, rotation=270\n- LEFT: patternId=Y, rotation=0\n- TOP: patternId=8, rotation=90\n- RIGHT: patternId=Q, rotation=90\n- FRONT: patternId=triangle, rotation=180\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C305/initial_net.png", "targetTopFaceImage": "images/C305/target_top_face.png"}, "__sample_id__": "C305"} +{"taskType": "roll_to_target_top_face", "code": "C306", "name": "Goal Roll C306", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "smile", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "heart", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "I", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "H", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "1", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_up", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "smile", "rotation": 90}, "FRONT": {"patternId": "heart", "rotation": 270}, "RIGHT": {"patternId": "I", "rotation": 180}, "BACK": {"patternId": "H", "rotation": 270}, "LEFT": {"patternId": "1", "rotation": 90}, "BOTTOM": {"patternId": "arrow_up", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "heart", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C306/initial_net.png", "targetTopFaceImage": "../images/C306/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 4, "targetRotationOffset": 90, "levelId": 306, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-306.json"}, "rollSequence": ["S", "N", "E", "N", "W", "W", "W", "N", "N"], "observedPathFaces": [{"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "N", "E", "N", "W", "W", "W", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "smile", "rotation": 90}, "FRONT": {"patternId": "heart", "rotation": 270}, "RIGHT": {"patternId": "I", "rotation": 180}, "BACK": {"patternId": "H", "rotation": 270}, "LEFT": {"patternId": "1", "rotation": 90}, "BOTTOM": {"patternId": "arrow_up", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C306\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=heart, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=H, rotation=270]\n[LEFT: patternId=1, rotation=90] [TOP: patternId=smile, rotation=90] [RIGHT: patternId=I, rotation=180]\n [FRONT: patternId=heart, rotation=270]\n [BOTTOM: patternId=arrow_up, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=H, rotation=270\n- LEFT: patternId=1, rotation=90\n- TOP: patternId=smile, rotation=90\n- RIGHT: patternId=I, rotation=180\n- FRONT: patternId=heart, rotation=270\n- BOTTOM: patternId=arrow_up, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C306/initial_net.png", "targetTopFaceImage": "images/C306/target_top_face.png"}, "__sample_id__": "C306"} +{"taskType": "roll_to_target_top_face", "code": "C307", "name": "Goal Roll C307", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "F", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "P", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "5", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "B", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "D", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "heart", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "F", "rotation": 0}, "FRONT": {"patternId": "P", "rotation": 270}, "RIGHT": {"patternId": "5", "rotation": 180}, "BACK": {"patternId": "B", "rotation": 270}, "LEFT": {"patternId": "D", "rotation": 270}, "BOTTOM": {"patternId": "heart", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "5", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C307/initial_net.png", "targetTopFaceImage": "../images/C307/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 6, "targetRotationOffset": 270, "levelId": 307, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-307.json"}, "rollSequence": ["W", "S", "S", "N", "W", "N", "N", "W", "S"], "observedPathFaces": [{"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "S", "N", "W", "N", "N", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "F", "rotation": 0}, "FRONT": {"patternId": "P", "rotation": 270}, "RIGHT": {"patternId": "5", "rotation": 180}, "BACK": {"patternId": "B", "rotation": 270}, "LEFT": {"patternId": "D", "rotation": 270}, "BOTTOM": {"patternId": "heart", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C307\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=5, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=B, rotation=270]\n[LEFT: patternId=D, rotation=270] [TOP: patternId=F, rotation=0] [RIGHT: patternId=5, rotation=180]\n [FRONT: patternId=P, rotation=270]\n [BOTTOM: patternId=heart, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=B, rotation=270\n- LEFT: patternId=D, rotation=270\n- TOP: patternId=F, rotation=0\n- RIGHT: patternId=5, rotation=180\n- FRONT: patternId=P, rotation=270\n- BOTTOM: patternId=heart, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C307/initial_net.png", "targetTopFaceImage": "images/C307/target_top_face.png"}, "__sample_id__": "C307"} +{"taskType": "roll_to_target_top_face", "code": "C308", "name": "Goal Roll C308", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "K", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "1", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_up", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "U", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "Q", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "K", "rotation": 0}, "FRONT": {"patternId": "1", "rotation": 0}, "RIGHT": {"patternId": "arrow_up", "rotation": 180}, "BACK": {"patternId": "U", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "Q", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "Q", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C308/initial_net.png", "targetTopFaceImage": "../images/C308/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 6, "targetRotationOffset": 270, "levelId": 308, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-308.json"}, "rollSequence": ["E", "E", "N", "W", "W", "S", "E", "E"], "observedPathFaces": [{"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "N", "W", "W", "S", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "K", "rotation": 0}, "FRONT": {"patternId": "1", "rotation": 0}, "RIGHT": {"patternId": "arrow_up", "rotation": 180}, "BACK": {"patternId": "U", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "Q", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C308\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=Q, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=U, rotation=270]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=K, rotation=0] [RIGHT: patternId=arrow_up, rotation=180]\n [FRONT: patternId=1, rotation=0]\n [BOTTOM: patternId=Q, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=U, rotation=270\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=K, rotation=0\n- RIGHT: patternId=arrow_up, rotation=180\n- FRONT: patternId=1, rotation=0\n- BOTTOM: patternId=Q, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C308/initial_net.png", "targetTopFaceImage": "images/C308/target_top_face.png"}, "__sample_id__": "C308"} +{"taskType": "roll_to_target_top_face", "code": "C309", "name": "Goal Roll C309", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "square", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "Y", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "6", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "P", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "3", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_left", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "square", "rotation": 90}, "FRONT": {"patternId": "Y", "rotation": 180}, "RIGHT": {"patternId": "6", "rotation": 0}, "BACK": {"patternId": "P", "rotation": 90}, "LEFT": {"patternId": "3", "rotation": 0}, "BOTTOM": {"patternId": "arrow_left", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "6", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C309/initial_net.png", "targetTopFaceImage": "../images/C309/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 309, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-309.json"}, "rollSequence": ["W", "N", "E", "N", "W", "E", "N", "E"], "observedPathFaces": [{"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "E", "N", "W", "E", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "square", "rotation": 90}, "FRONT": {"patternId": "Y", "rotation": 180}, "RIGHT": {"patternId": "6", "rotation": 0}, "BACK": {"patternId": "P", "rotation": 90}, "LEFT": {"patternId": "3", "rotation": 0}, "BOTTOM": {"patternId": "arrow_left", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C309\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=6, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=P, rotation=90]\n[LEFT: patternId=3, rotation=0] [TOP: patternId=square, rotation=90] [RIGHT: patternId=6, rotation=0]\n [FRONT: patternId=Y, rotation=180]\n [BOTTOM: patternId=arrow_left, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=P, rotation=90\n- LEFT: patternId=3, rotation=0\n- TOP: patternId=square, rotation=90\n- RIGHT: patternId=6, rotation=0\n- FRONT: patternId=Y, rotation=180\n- BOTTOM: patternId=arrow_left, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C309/initial_net.png", "targetTopFaceImage": "images/C309/target_top_face.png"}, "__sample_id__": "C309"} +{"taskType": "roll_to_target_top_face", "code": "C310", "name": "Goal Roll C310", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "K", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "W", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "triangle", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "M", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "F", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "K", "rotation": 180}, "FRONT": {"patternId": "W", "rotation": 90}, "RIGHT": {"patternId": "triangle", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "M", "rotation": 270}, "BOTTOM": {"patternId": "F", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "triangle", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C310/initial_net.png", "targetTopFaceImage": "../images/C310/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 310, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-310.json"}, "rollSequence": ["W", "S", "W", "S", "E", "S", "E", "N"], "observedPathFaces": [{"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "W", "S", "E", "S", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "K", "rotation": 180}, "FRONT": {"patternId": "W", "rotation": 90}, "RIGHT": {"patternId": "triangle", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "M", "rotation": 270}, "BOTTOM": {"patternId": "F", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C310\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=triangle, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=M, rotation=270] [TOP: patternId=K, rotation=180] [RIGHT: patternId=triangle, rotation=180]\n [FRONT: patternId=W, rotation=90]\n [BOTTOM: patternId=F, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=M, rotation=270\n- TOP: patternId=K, rotation=180\n- RIGHT: patternId=triangle, rotation=180\n- FRONT: patternId=W, rotation=90\n- BOTTOM: patternId=F, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C310/initial_net.png", "targetTopFaceImage": "images/C310/target_top_face.png"}, "__sample_id__": "C310"} +{"taskType": "roll_to_target_top_face", "code": "C311", "name": "Goal Roll C311", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "C", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "P", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "R", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "7", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "F", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "square", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "C", "rotation": 0}, "FRONT": {"patternId": "P", "rotation": 270}, "RIGHT": {"patternId": "R", "rotation": 180}, "BACK": {"patternId": "7", "rotation": 90}, "LEFT": {"patternId": "F", "rotation": 90}, "BOTTOM": {"patternId": "square", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "F", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C311/initial_net.png", "targetTopFaceImage": "../images/C311/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 311, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-311.json"}, "rollSequence": ["E", "N", "N", "E", "E", "W", "N", "W", "N"], "observedPathFaces": [{"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "N", "E", "E", "W", "N", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "C", "rotation": 0}, "FRONT": {"patternId": "P", "rotation": 270}, "RIGHT": {"patternId": "R", "rotation": 180}, "BACK": {"patternId": "7", "rotation": 90}, "LEFT": {"patternId": "F", "rotation": 90}, "BOTTOM": {"patternId": "square", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C311\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=F, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=7, rotation=90]\n[LEFT: patternId=F, rotation=90] [TOP: patternId=C, rotation=0] [RIGHT: patternId=R, rotation=180]\n [FRONT: patternId=P, rotation=270]\n [BOTTOM: patternId=square, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=7, rotation=90\n- LEFT: patternId=F, rotation=90\n- TOP: patternId=C, rotation=0\n- RIGHT: patternId=R, rotation=180\n- FRONT: patternId=P, rotation=270\n- BOTTOM: patternId=square, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C311/initial_net.png", "targetTopFaceImage": "images/C311/target_top_face.png"}, "__sample_id__": "C311"} +{"taskType": "roll_to_target_top_face", "code": "C312", "name": "Goal Roll C312", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "T", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "4", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_left", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "O", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "F", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "T", "rotation": 270}, "FRONT": {"patternId": "4", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 180}, "LEFT": {"patternId": "O", "rotation": 0}, "BOTTOM": {"patternId": "F", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 7, "stepNumber": 8, "patternId": "T", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C312/initial_net.png", "targetTopFaceImage": "../images/C312/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 8, "targetRotationOffset": 270, "levelId": 312, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-312.json"}, "rollSequence": ["W", "S", "W", "N", "N", "S", "W", "N"], "observedPathFaces": [{"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "W", "N", "N", "S", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "T", "rotation": 270}, "FRONT": {"patternId": "4", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 180}, "LEFT": {"patternId": "O", "rotation": 0}, "BOTTOM": {"patternId": "F", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C312\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=T, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_left, rotation=180]\n[LEFT: patternId=O, rotation=0] [TOP: patternId=T, rotation=270] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=4, rotation=0]\n [BOTTOM: patternId=F, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_left, rotation=180\n- LEFT: patternId=O, rotation=0\n- TOP: patternId=T, rotation=270\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=4, rotation=0\n- BOTTOM: patternId=F, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C312/initial_net.png", "targetTopFaceImage": "images/C312/target_top_face.png"}, "__sample_id__": "C312"} +{"taskType": "roll_to_target_top_face", "code": "C313", "name": "Goal Roll C313", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "plus", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "N", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "B", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "W", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "O", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "plus", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "N", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 270}, "LEFT": {"patternId": "W", "rotation": 180}, "BOTTOM": {"patternId": "O", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 6, "stepNumber": 7, "patternId": "N", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C313/initial_net.png", "targetTopFaceImage": "../images/C313/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 7, "targetRotationOffset": 180, "levelId": 313, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-313.json"}, "rollSequence": ["W", "N", "N", "E", "S", "S", "E", "E"], "observedPathFaces": [{"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "N", "E", "S", "S", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "plus", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "N", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 270}, "LEFT": {"patternId": "W", "rotation": 180}, "BOTTOM": {"patternId": "O", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C313\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=N, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=B, rotation=270]\n[LEFT: patternId=W, rotation=180] [TOP: patternId=plus, rotation=90] [RIGHT: patternId=N, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=O, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=B, rotation=270\n- LEFT: patternId=W, rotation=180\n- TOP: patternId=plus, rotation=90\n- RIGHT: patternId=N, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=O, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C313/initial_net.png", "targetTopFaceImage": "images/C313/target_top_face.png"}, "__sample_id__": "C313"} +{"taskType": "roll_to_target_top_face", "code": "C314", "name": "Goal Roll C314", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "G", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "square", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "B", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "K", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "J", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "1", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "G", "rotation": 270}, "FRONT": {"patternId": "square", "rotation": 270}, "RIGHT": {"patternId": "B", "rotation": 180}, "BACK": {"patternId": "K", "rotation": 180}, "LEFT": {"patternId": "J", "rotation": 0}, "BOTTOM": {"patternId": "1", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "G", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C314/initial_net.png", "targetTopFaceImage": "../images/C314/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 2, "targetRotationOffset": 180, "levelId": 314, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-314.json"}, "rollSequence": ["S", "N", "E", "N", "N", "W", "N", "N"], "observedPathFaces": [{"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "N", "E", "N", "N", "W", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "G", "rotation": 270}, "FRONT": {"patternId": "square", "rotation": 270}, "RIGHT": {"patternId": "B", "rotation": 180}, "BACK": {"patternId": "K", "rotation": 180}, "LEFT": {"patternId": "J", "rotation": 0}, "BOTTOM": {"patternId": "1", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C314\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=G, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=K, rotation=180]\n[LEFT: patternId=J, rotation=0] [TOP: patternId=G, rotation=270] [RIGHT: patternId=B, rotation=180]\n [FRONT: patternId=square, rotation=270]\n [BOTTOM: patternId=1, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=K, rotation=180\n- LEFT: patternId=J, rotation=0\n- TOP: patternId=G, rotation=270\n- RIGHT: patternId=B, rotation=180\n- FRONT: patternId=square, rotation=270\n- BOTTOM: patternId=1, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C314/initial_net.png", "targetTopFaceImage": "images/C314/target_top_face.png"}, "__sample_id__": "C314"} +{"taskType": "roll_to_target_top_face", "code": "C315", "name": "Goal Roll C315", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "Q", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "M", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "heart", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "triangle", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "O", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "5", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "Q", "rotation": 90}, "FRONT": {"patternId": "M", "rotation": 180}, "RIGHT": {"patternId": "heart", "rotation": 90}, "BACK": {"patternId": "triangle", "rotation": 270}, "LEFT": {"patternId": "O", "rotation": 270}, "BOTTOM": {"patternId": "5", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "heart", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C315/initial_net.png", "targetTopFaceImage": "../images/C315/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 4, "targetRotationOffset": 180, "levelId": 315, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-315.json"}, "rollSequence": ["N", "E", "S", "S", "N", "E", "S", "E"], "observedPathFaces": [{"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "S", "S", "N", "E", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "Q", "rotation": 90}, "FRONT": {"patternId": "M", "rotation": 180}, "RIGHT": {"patternId": "heart", "rotation": 90}, "BACK": {"patternId": "triangle", "rotation": 270}, "LEFT": {"patternId": "O", "rotation": 270}, "BOTTOM": {"patternId": "5", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C315\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=heart, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=triangle, rotation=270]\n[LEFT: patternId=O, rotation=270] [TOP: patternId=Q, rotation=90] [RIGHT: patternId=heart, rotation=90]\n [FRONT: patternId=M, rotation=180]\n [BOTTOM: patternId=5, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=triangle, rotation=270\n- LEFT: patternId=O, rotation=270\n- TOP: patternId=Q, rotation=90\n- RIGHT: patternId=heart, rotation=90\n- FRONT: patternId=M, rotation=180\n- BOTTOM: patternId=5, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C315/initial_net.png", "targetTopFaceImage": "images/C315/target_top_face.png"}, "__sample_id__": "C315"} +{"taskType": "roll_to_target_top_face", "code": "C316", "name": "Goal Roll C316", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "A", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "7", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Q", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "1", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_down", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "B", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "A", "rotation": 270}, "FRONT": {"patternId": "7", "rotation": 270}, "RIGHT": {"patternId": "Q", "rotation": 0}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "arrow_down", "rotation": 90}, "BOTTOM": {"patternId": "B", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "B", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C316/initial_net.png", "targetTopFaceImage": "../images/C316/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 2, "targetRotationOffset": 270, "levelId": 316, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-316.json"}, "rollSequence": ["N", "N", "N", "E", "N", "E", "E", "N"], "observedPathFaces": [{"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "N", "E", "N", "E", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "A", "rotation": 270}, "FRONT": {"patternId": "7", "rotation": 270}, "RIGHT": {"patternId": "Q", "rotation": 0}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "arrow_down", "rotation": 90}, "BOTTOM": {"patternId": "B", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C316\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=B, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=1, rotation=180]\n[LEFT: patternId=arrow_down, rotation=90] [TOP: patternId=A, rotation=270] [RIGHT: patternId=Q, rotation=0]\n [FRONT: patternId=7, rotation=270]\n [BOTTOM: patternId=B, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=1, rotation=180\n- LEFT: patternId=arrow_down, rotation=90\n- TOP: patternId=A, rotation=270\n- RIGHT: patternId=Q, rotation=0\n- FRONT: patternId=7, rotation=270\n- BOTTOM: patternId=B, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C316/initial_net.png", "targetTopFaceImage": "images/C316/target_top_face.png"}, "__sample_id__": "C316"} +{"taskType": "roll_to_target_top_face", "code": "C317", "name": "Goal Roll C317", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "6", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "9", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "F", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "diamond", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "6", "rotation": 180}, "FRONT": {"patternId": "9", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "F", "rotation": 180}, "BOTTOM": {"patternId": "diamond", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "6", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C317/initial_net.png", "targetTopFaceImage": "../images/C317/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 4, "targetRotationOffset": 270, "levelId": 317, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-317.json"}, "rollSequence": ["S", "W", "E", "N", "W", "E", "S", "S", "W"], "observedPathFaces": [{"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "E", "N", "W", "E", "S", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "6", "rotation": 180}, "FRONT": {"patternId": "9", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "F", "rotation": 180}, "BOTTOM": {"patternId": "diamond", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C317\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=6, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=F, rotation=180] [TOP: patternId=6, rotation=180] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=9, rotation=180]\n [BOTTOM: patternId=diamond, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=F, rotation=180\n- TOP: patternId=6, rotation=180\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=9, rotation=180\n- BOTTOM: patternId=diamond, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C317/initial_net.png", "targetTopFaceImage": "images/C317/target_top_face.png"}, "__sample_id__": "C317"} +{"taskType": "roll_to_target_top_face", "code": "C318", "name": "Goal Roll C318", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "9", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "I", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "F", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_down", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "9", "rotation": 180}, "RIGHT": {"patternId": "I", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "F", "rotation": 0}, "BOTTOM": {"patternId": "arrow_down", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "F", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C318/initial_net.png", "targetTopFaceImage": "../images/C318/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 3, "targetRotationOffset": 90, "levelId": 318, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-318.json"}, "rollSequence": ["S", "N", "E", "S", "S", "W", "W", "N", "N"], "observedPathFaces": [{"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "N", "E", "S", "S", "W", "W", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "9", "rotation": 180}, "RIGHT": {"patternId": "I", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "F", "rotation": 0}, "BOTTOM": {"patternId": "arrow_down", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C318\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=F, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=F, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=I, rotation=90]\n [FRONT: patternId=9, rotation=180]\n [BOTTOM: patternId=arrow_down, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=F, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=I, rotation=90\n- FRONT: patternId=9, rotation=180\n- BOTTOM: patternId=arrow_down, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C318/initial_net.png", "targetTopFaceImage": "images/C318/target_top_face.png"}, "__sample_id__": "C318"} +{"taskType": "roll_to_target_top_face", "code": "C319", "name": "Goal Roll C319", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "X", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "C", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "1", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "heart", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "O", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "8", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "X", "rotation": 270}, "FRONT": {"patternId": "C", "rotation": 180}, "RIGHT": {"patternId": "1", "rotation": 90}, "BACK": {"patternId": "heart", "rotation": 0}, "LEFT": {"patternId": "O", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "O", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C319/initial_net.png", "targetTopFaceImage": "../images/C319/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 4, "targetRotationOffset": 270, "levelId": 319, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-319.json"}, "rollSequence": ["W", "W", "N", "W", "N", "N", "N", "W", "S"], "observedPathFaces": [{"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "N", "W", "N", "N", "N", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "X", "rotation": 270}, "FRONT": {"patternId": "C", "rotation": 180}, "RIGHT": {"patternId": "1", "rotation": 90}, "BACK": {"patternId": "heart", "rotation": 0}, "LEFT": {"patternId": "O", "rotation": 0}, "BOTTOM": {"patternId": "8", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C319\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=O, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=heart, rotation=0]\n[LEFT: patternId=O, rotation=0] [TOP: patternId=X, rotation=270] [RIGHT: patternId=1, rotation=90]\n [FRONT: patternId=C, rotation=180]\n [BOTTOM: patternId=8, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=heart, rotation=0\n- LEFT: patternId=O, rotation=0\n- TOP: patternId=X, rotation=270\n- RIGHT: patternId=1, rotation=90\n- FRONT: patternId=C, rotation=180\n- BOTTOM: patternId=8, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C319/initial_net.png", "targetTopFaceImage": "images/C319/target_top_face.png"}, "__sample_id__": "C319"} +{"taskType": "roll_to_target_top_face", "code": "C320", "name": "Goal Roll C320", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "S", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "U", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "3", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "6", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "W", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "S", "rotation": 0}, "FRONT": {"patternId": "U", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "3", "rotation": 270}, "LEFT": {"patternId": "6", "rotation": 180}, "BOTTOM": {"patternId": "W", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 7, "stepNumber": 8, "patternId": "U", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C320/initial_net.png", "targetTopFaceImage": "../images/C320/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 8, "targetRotationOffset": 270, "levelId": 320, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-320.json"}, "rollSequence": ["W", "N", "S", "S", "W", "N", "N", "W"], "observedPathFaces": [{"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "S", "S", "W", "N", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "S", "rotation": 0}, "FRONT": {"patternId": "U", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "3", "rotation": 270}, "LEFT": {"patternId": "6", "rotation": 180}, "BOTTOM": {"patternId": "W", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C320\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=U, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=3, rotation=270]\n[LEFT: patternId=6, rotation=180] [TOP: patternId=S, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=U, rotation=270]\n [BOTTOM: patternId=W, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=3, rotation=270\n- LEFT: patternId=6, rotation=180\n- TOP: patternId=S, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=U, rotation=270\n- BOTTOM: patternId=W, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C320/initial_net.png", "targetTopFaceImage": "images/C320/target_top_face.png"}, "__sample_id__": "C320"} +{"taskType": "roll_to_target_top_face", "code": "C321", "name": "Goal Roll C321", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "O", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "smile", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "T", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "X", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "I", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "diamond", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "O", "rotation": 0}, "FRONT": {"patternId": "smile", "rotation": 270}, "RIGHT": {"patternId": "T", "rotation": 180}, "BACK": {"patternId": "X", "rotation": 270}, "LEFT": {"patternId": "I", "rotation": 180}, "BOTTOM": {"patternId": "diamond", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "smile", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C321/initial_net.png", "targetTopFaceImage": "../images/C321/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 3, "targetRotationOffset": 270, "levelId": 321, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-321.json"}, "rollSequence": ["S", "E", "E", "E", "N", "S", "S", "W"], "observedPathFaces": [{"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "E", "E", "N", "S", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 0}, "FRONT": {"patternId": "smile", "rotation": 270}, "RIGHT": {"patternId": "T", "rotation": 180}, "BACK": {"patternId": "X", "rotation": 270}, "LEFT": {"patternId": "I", "rotation": 180}, "BOTTOM": {"patternId": "diamond", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C321\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=smile, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=X, rotation=270]\n[LEFT: patternId=I, rotation=180] [TOP: patternId=O, rotation=0] [RIGHT: patternId=T, rotation=180]\n [FRONT: patternId=smile, rotation=270]\n [BOTTOM: patternId=diamond, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=X, rotation=270\n- LEFT: patternId=I, rotation=180\n- TOP: patternId=O, rotation=0\n- RIGHT: patternId=T, rotation=180\n- FRONT: patternId=smile, rotation=270\n- BOTTOM: patternId=diamond, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C321/initial_net.png", "targetTopFaceImage": "images/C321/target_top_face.png"}, "__sample_id__": "C321"} +{"taskType": "roll_to_target_top_face", "code": "C322", "name": "Goal Roll C322", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "circle", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "star", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "heart", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "B", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "T", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "J", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "circle", "rotation": 0}, "FRONT": {"patternId": "star", "rotation": 0}, "RIGHT": {"patternId": "heart", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 90}, "LEFT": {"patternId": "T", "rotation": 180}, "BOTTOM": {"patternId": "J", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "J", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C322/initial_net.png", "targetTopFaceImage": "../images/C322/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 6, "targetRotationOffset": 90, "levelId": 322, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-322.json"}, "rollSequence": ["N", "S", "W", "E", "W", "W", "S", "N", "W"], "observedPathFaces": [{"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "S", "W", "E", "W", "W", "S", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "circle", "rotation": 0}, "FRONT": {"patternId": "star", "rotation": 0}, "RIGHT": {"patternId": "heart", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 90}, "LEFT": {"patternId": "T", "rotation": 180}, "BOTTOM": {"patternId": "J", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C322\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=J, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=B, rotation=90]\n[LEFT: patternId=T, rotation=180] [TOP: patternId=circle, rotation=0] [RIGHT: patternId=heart, rotation=0]\n [FRONT: patternId=star, rotation=0]\n [BOTTOM: patternId=J, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=B, rotation=90\n- LEFT: patternId=T, rotation=180\n- TOP: patternId=circle, rotation=0\n- RIGHT: patternId=heart, rotation=0\n- FRONT: patternId=star, rotation=0\n- BOTTOM: patternId=J, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C322/initial_net.png", "targetTopFaceImage": "images/C322/target_top_face.png"}, "__sample_id__": "C322"} +{"taskType": "roll_to_target_top_face", "code": "C323", "name": "Goal Roll C323", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "arrow_left", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "P", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "9", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_down", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "T", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "D", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "arrow_left", "rotation": 270}, "FRONT": {"patternId": "P", "rotation": 180}, "RIGHT": {"patternId": "9", "rotation": 0}, "BACK": {"patternId": "arrow_down", "rotation": 90}, "LEFT": {"patternId": "T", "rotation": 270}, "BOTTOM": {"patternId": "D", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "P", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C323/initial_net.png", "targetTopFaceImage": "../images/C323/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 6, "targetRotationOffset": 180, "levelId": 323, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-323.json"}, "rollSequence": ["E", "N", "W", "W", "S", "S", "W", "W", "S"], "observedPathFaces": [{"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "W", "W", "S", "S", "W", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "arrow_left", "rotation": 270}, "FRONT": {"patternId": "P", "rotation": 180}, "RIGHT": {"patternId": "9", "rotation": 0}, "BACK": {"patternId": "arrow_down", "rotation": 90}, "LEFT": {"patternId": "T", "rotation": 270}, "BOTTOM": {"patternId": "D", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C323\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=P, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_down, rotation=90]\n[LEFT: patternId=T, rotation=270] [TOP: patternId=arrow_left, rotation=270] [RIGHT: patternId=9, rotation=0]\n [FRONT: patternId=P, rotation=180]\n [BOTTOM: patternId=D, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_down, rotation=90\n- LEFT: patternId=T, rotation=270\n- TOP: patternId=arrow_left, rotation=270\n- RIGHT: patternId=9, rotation=0\n- FRONT: patternId=P, rotation=180\n- BOTTOM: patternId=D, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C323/initial_net.png", "targetTopFaceImage": "images/C323/target_top_face.png"}, "__sample_id__": "C323"} +{"taskType": "roll_to_target_top_face", "code": "C324", "name": "Goal Roll C324", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "Z", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "2", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Y", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "L", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "W", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "Z", "rotation": 270}, "FRONT": {"patternId": "2", "rotation": 270}, "RIGHT": {"patternId": "Y", "rotation": 0}, "BACK": {"patternId": "L", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "W", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "W", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C324/initial_net.png", "targetTopFaceImage": "../images/C324/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 2, "targetRotationOffset": 180, "levelId": 324, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-324.json"}, "rollSequence": ["E", "E", "S", "S", "W", "S", "N", "W"], "observedPathFaces": [{"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "S", "S", "W", "S", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "Z", "rotation": 270}, "FRONT": {"patternId": "2", "rotation": 270}, "RIGHT": {"patternId": "Y", "rotation": 0}, "BACK": {"patternId": "L", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "W", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C324\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=W, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=L, rotation=270]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=Z, rotation=270] [RIGHT: patternId=Y, rotation=0]\n [FRONT: patternId=2, rotation=270]\n [BOTTOM: patternId=W, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=L, rotation=270\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=Z, rotation=270\n- RIGHT: patternId=Y, rotation=0\n- FRONT: patternId=2, rotation=270\n- BOTTOM: patternId=W, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C324/initial_net.png", "targetTopFaceImage": "images/C324/target_top_face.png"}, "__sample_id__": "C324"} +{"taskType": "roll_to_target_top_face", "code": "C325", "name": "Goal Roll C325", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "M", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "D", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "I", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "T", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_left", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "M", "rotation": 90}, "FRONT": {"patternId": "D", "rotation": 270}, "RIGHT": {"patternId": "I", "rotation": 90}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 6, "stepNumber": 7, "patternId": "D", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C325/initial_net.png", "targetTopFaceImage": "../images/C325/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 7, "targetRotationOffset": 270, "levelId": 325, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-325.json"}, "rollSequence": ["E", "S", "E", "E", "E", "N", "W", "S"], "observedPathFaces": [{"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "E", "E", "E", "N", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "M", "rotation": 90}, "FRONT": {"patternId": "D", "rotation": 270}, "RIGHT": {"patternId": "I", "rotation": 90}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C325\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=D, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=T, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=M, rotation=90] [RIGHT: patternId=I, rotation=90]\n [FRONT: patternId=D, rotation=270]\n [BOTTOM: patternId=arrow_left, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=T, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=M, rotation=90\n- RIGHT: patternId=I, rotation=90\n- FRONT: patternId=D, rotation=270\n- BOTTOM: patternId=arrow_left, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C325/initial_net.png", "targetTopFaceImage": "images/C325/target_top_face.png"}, "__sample_id__": "C325"} +{"taskType": "roll_to_target_top_face", "code": "C326", "name": "Goal Roll C326", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "4", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "M", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "I", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "star", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "O", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "diamond", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "4", "rotation": 90}, "FRONT": {"patternId": "M", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 0}, "LEFT": {"patternId": "O", "rotation": 270}, "BOTTOM": {"patternId": "diamond", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "star", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C326/initial_net.png", "targetTopFaceImage": "../images/C326/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 2, "targetRotationOffset": 90, "levelId": 326, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-326.json"}, "rollSequence": ["E", "S", "S", "E", "N", "E", "N", "E", "N"], "observedPathFaces": [{"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "S", "E", "N", "E", "N", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "4", "rotation": 90}, "FRONT": {"patternId": "M", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 0}, "LEFT": {"patternId": "O", "rotation": 270}, "BOTTOM": {"patternId": "diamond", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C326\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=star, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=star, rotation=0]\n[LEFT: patternId=O, rotation=270] [TOP: patternId=4, rotation=90] [RIGHT: patternId=I, rotation=0]\n [FRONT: patternId=M, rotation=0]\n [BOTTOM: patternId=diamond, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=star, rotation=0\n- LEFT: patternId=O, rotation=270\n- TOP: patternId=4, rotation=90\n- RIGHT: patternId=I, rotation=0\n- FRONT: patternId=M, rotation=0\n- BOTTOM: patternId=diamond, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C326/initial_net.png", "targetTopFaceImage": "images/C326/target_top_face.png"}, "__sample_id__": "C326"} +{"taskType": "roll_to_target_top_face", "code": "C327", "name": "Goal Roll C327", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "G", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "C", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "V", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "H", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "X", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "G", "rotation": 0}, "FRONT": {"patternId": "C", "rotation": 270}, "RIGHT": {"patternId": "V", "rotation": 90}, "BACK": {"patternId": "H", "rotation": 180}, "LEFT": {"patternId": "X", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "C", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C327/initial_net.png", "targetTopFaceImage": "../images/C327/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 2, "targetRotationOffset": 90, "levelId": 327, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-327.json"}, "rollSequence": ["E", "N", "E", "N", "E", "W", "S", "S", "E"], "observedPathFaces": [{"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "E", "N", "E", "W", "S", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "G", "rotation": 0}, "FRONT": {"patternId": "C", "rotation": 270}, "RIGHT": {"patternId": "V", "rotation": 90}, "BACK": {"patternId": "H", "rotation": 180}, "LEFT": {"patternId": "X", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C327\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=C, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=H, rotation=180]\n[LEFT: patternId=X, rotation=0] [TOP: patternId=G, rotation=0] [RIGHT: patternId=V, rotation=90]\n [FRONT: patternId=C, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=H, rotation=180\n- LEFT: patternId=X, rotation=0\n- TOP: patternId=G, rotation=0\n- RIGHT: patternId=V, rotation=90\n- FRONT: patternId=C, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C327/initial_net.png", "targetTopFaceImage": "images/C327/target_top_face.png"}, "__sample_id__": "C327"} +{"taskType": "roll_to_target_top_face", "code": "C328", "name": "Goal Roll C328", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "K", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "F", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "M", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "8", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "8", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "K", "rotation": 90}, "FRONT": {"patternId": "F", "rotation": 0}, "RIGHT": {"patternId": "M", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 180}, "BOTTOM": {"patternId": "8", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "8", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C328/initial_net.png", "targetTopFaceImage": "../images/C328/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 3, "targetRotationOffset": 270, "levelId": 328, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-328.json"}, "rollSequence": ["S", "E", "S", "W", "W", "E", "S", "W", "W"], "observedPathFaces": [{"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "S", "W", "W", "E", "S", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "K", "rotation": 90}, "FRONT": {"patternId": "F", "rotation": 0}, "RIGHT": {"patternId": "M", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 180}, "BOTTOM": {"patternId": "8", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C328\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=8, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=8, rotation=180] [TOP: patternId=K, rotation=90] [RIGHT: patternId=M, rotation=90]\n [FRONT: patternId=F, rotation=0]\n [BOTTOM: patternId=8, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=8, rotation=180\n- TOP: patternId=K, rotation=90\n- RIGHT: patternId=M, rotation=90\n- FRONT: patternId=F, rotation=0\n- BOTTOM: patternId=8, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C328/initial_net.png", "targetTopFaceImage": "images/C328/target_top_face.png"}, "__sample_id__": "C328"} +{"taskType": "roll_to_target_top_face", "code": "C329", "name": "Goal Roll C329", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "arrow_right", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "square", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "circle", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "T", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_down", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "arrow_right", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 90}, "RIGHT": {"patternId": "circle", "rotation": 270}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "arrow_down", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "square", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C329/initial_net.png", "targetTopFaceImage": "../images/C329/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 3, "targetRotationOffset": 270, "levelId": 329, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-329.json"}, "rollSequence": ["S", "W", "W", "S", "W", "S", "S", "S"], "observedPathFaces": [{"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "W", "S", "W", "S", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "arrow_right", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 90}, "RIGHT": {"patternId": "circle", "rotation": 270}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "arrow_down", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C329\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=square, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=T, rotation=180]\n[LEFT: patternId=arrow_down, rotation=270] [TOP: patternId=arrow_right, rotation=0] [RIGHT: patternId=circle, rotation=270]\n [FRONT: patternId=square, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=T, rotation=180\n- LEFT: patternId=arrow_down, rotation=270\n- TOP: patternId=arrow_right, rotation=0\n- RIGHT: patternId=circle, rotation=270\n- FRONT: patternId=square, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C329/initial_net.png", "targetTopFaceImage": "images/C329/target_top_face.png"}, "__sample_id__": "C329"} +{"taskType": "roll_to_target_top_face", "code": "C330", "name": "Goal Roll C330", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "S", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "T", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "G", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "J", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "W", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "S", "rotation": 180}, "FRONT": {"patternId": "T", "rotation": 270}, "RIGHT": {"patternId": "G", "rotation": 90}, "BACK": {"patternId": "J", "rotation": 90}, "LEFT": {"patternId": "W", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 7, "stepNumber": 8, "patternId": "W", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C330/initial_net.png", "targetTopFaceImage": "../images/C330/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 8, "targetRotationOffset": 180, "levelId": 330, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-330.json"}, "rollSequence": ["W", "N", "N", "W", "W", "N", "E", "N"], "observedPathFaces": [{"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "N", "W", "W", "N", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "S", "rotation": 180}, "FRONT": {"patternId": "T", "rotation": 270}, "RIGHT": {"patternId": "G", "rotation": 90}, "BACK": {"patternId": "J", "rotation": 90}, "LEFT": {"patternId": "W", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C330\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=W, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=J, rotation=90]\n[LEFT: patternId=W, rotation=90] [TOP: patternId=S, rotation=180] [RIGHT: patternId=G, rotation=90]\n [FRONT: patternId=T, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=J, rotation=90\n- LEFT: patternId=W, rotation=90\n- TOP: patternId=S, rotation=180\n- RIGHT: patternId=G, rotation=90\n- FRONT: patternId=T, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C330/initial_net.png", "targetTopFaceImage": "images/C330/target_top_face.png"}, "__sample_id__": "C330"} +{"taskType": "roll_to_target_top_face", "code": "C331", "name": "Goal Roll C331", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "E", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "2", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "B", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "1", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "S", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_right", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "E", "rotation": 270}, "FRONT": {"patternId": "2", "rotation": 90}, "RIGHT": {"patternId": "B", "rotation": 0}, "BACK": {"patternId": "1", "rotation": 0}, "LEFT": {"patternId": "S", "rotation": 90}, "BOTTOM": {"patternId": "arrow_right", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "arrow_right", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C331/initial_net.png", "targetTopFaceImage": "../images/C331/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 5, "targetRotationOffset": 270, "levelId": 331, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-331.json"}, "rollSequence": ["S", "E", "N", "N", "N", "E", "N", "E", "N"], "observedPathFaces": [{"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "N", "N", "N", "E", "N", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "E", "rotation": 270}, "FRONT": {"patternId": "2", "rotation": 90}, "RIGHT": {"patternId": "B", "rotation": 0}, "BACK": {"patternId": "1", "rotation": 0}, "LEFT": {"patternId": "S", "rotation": 90}, "BOTTOM": {"patternId": "arrow_right", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C331\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=arrow_right, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=1, rotation=0]\n[LEFT: patternId=S, rotation=90] [TOP: patternId=E, rotation=270] [RIGHT: patternId=B, rotation=0]\n [FRONT: patternId=2, rotation=90]\n [BOTTOM: patternId=arrow_right, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=1, rotation=0\n- LEFT: patternId=S, rotation=90\n- TOP: patternId=E, rotation=270\n- RIGHT: patternId=B, rotation=0\n- FRONT: patternId=2, rotation=90\n- BOTTOM: patternId=arrow_right, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C331/initial_net.png", "targetTopFaceImage": "images/C331/target_top_face.png"}, "__sample_id__": "C331"} +{"taskType": "roll_to_target_top_face", "code": "C332", "name": "Goal Roll C332", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "N", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "T", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "O", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "diamond", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "square", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "Y", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "N", "rotation": 0}, "FRONT": {"patternId": "T", "rotation": 90}, "RIGHT": {"patternId": "O", "rotation": 0}, "BACK": {"patternId": "diamond", "rotation": 90}, "LEFT": {"patternId": "square", "rotation": 180}, "BOTTOM": {"patternId": "Y", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "N", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C332/initial_net.png", "targetTopFaceImage": "../images/C332/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 6, "targetRotationOffset": 270, "levelId": 332, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-332.json"}, "rollSequence": ["W", "N", "N", "W", "E", "E", "N", "N", "W"], "observedPathFaces": [{"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "N", "W", "E", "E", "N", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "N", "rotation": 0}, "FRONT": {"patternId": "T", "rotation": 90}, "RIGHT": {"patternId": "O", "rotation": 0}, "BACK": {"patternId": "diamond", "rotation": 90}, "LEFT": {"patternId": "square", "rotation": 180}, "BOTTOM": {"patternId": "Y", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C332\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=N, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=diamond, rotation=90]\n[LEFT: patternId=square, rotation=180] [TOP: patternId=N, rotation=0] [RIGHT: patternId=O, rotation=0]\n [FRONT: patternId=T, rotation=90]\n [BOTTOM: patternId=Y, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=diamond, rotation=90\n- LEFT: patternId=square, rotation=180\n- TOP: patternId=N, rotation=0\n- RIGHT: patternId=O, rotation=0\n- FRONT: patternId=T, rotation=90\n- BOTTOM: patternId=Y, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C332/initial_net.png", "targetTopFaceImage": "images/C332/target_top_face.png"}, "__sample_id__": "C332"} +{"taskType": "roll_to_target_top_face", "code": "C333", "name": "Goal Roll C333", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "A", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "7", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "8", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "diamond", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "6", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "A", "rotation": 180}, "RIGHT": {"patternId": "7", "rotation": 270}, "BACK": {"patternId": "8", "rotation": 90}, "LEFT": {"patternId": "diamond", "rotation": 180}, "BOTTOM": {"patternId": "6", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "diamond", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C333/initial_net.png", "targetTopFaceImage": "../images/C333/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 2, "targetRotationOffset": 270, "levelId": 333, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-333.json"}, "rollSequence": ["S", "E", "E", "W", "N", "N", "E", "E"], "observedPathFaces": [{"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "E", "W", "N", "N", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "A", "rotation": 180}, "RIGHT": {"patternId": "7", "rotation": 270}, "BACK": {"patternId": "8", "rotation": 90}, "LEFT": {"patternId": "diamond", "rotation": 180}, "BOTTOM": {"patternId": "6", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C333\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=diamond, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=8, rotation=90]\n[LEFT: patternId=diamond, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=7, rotation=270]\n [FRONT: patternId=A, rotation=180]\n [BOTTOM: patternId=6, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=8, rotation=90\n- LEFT: patternId=diamond, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=7, rotation=270\n- FRONT: patternId=A, rotation=180\n- BOTTOM: patternId=6, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C333/initial_net.png", "targetTopFaceImage": "images/C333/target_top_face.png"}, "__sample_id__": "C333"} +{"taskType": "roll_to_target_top_face", "code": "C334", "name": "Goal Roll C334", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "O", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "O", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Q", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "smile", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "V", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "O", "rotation": 180}, "FRONT": {"patternId": "O", "rotation": 180}, "RIGHT": {"patternId": "Q", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "smile", "rotation": 0}, "BOTTOM": {"patternId": "V", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "Q", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C334/initial_net.png", "targetTopFaceImage": "../images/C334/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 5, "targetRotationOffset": 180, "levelId": 334, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-334.json"}, "rollSequence": ["S", "E", "N", "W", "N", "W", "W", "S"], "observedPathFaces": [{"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "N", "W", "N", "W", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 180}, "FRONT": {"patternId": "O", "rotation": 180}, "RIGHT": {"patternId": "Q", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "smile", "rotation": 0}, "BOTTOM": {"patternId": "V", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C334\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=Q, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=smile, rotation=0] [TOP: patternId=O, rotation=180] [RIGHT: patternId=Q, rotation=90]\n [FRONT: patternId=O, rotation=180]\n [BOTTOM: patternId=V, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=smile, rotation=0\n- TOP: patternId=O, rotation=180\n- RIGHT: patternId=Q, rotation=90\n- FRONT: patternId=O, rotation=180\n- BOTTOM: patternId=V, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C334/initial_net.png", "targetTopFaceImage": "images/C334/target_top_face.png"}, "__sample_id__": "C334"} +{"taskType": "roll_to_target_top_face", "code": "C335", "name": "Goal Roll C335", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "I", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "6", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "4", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "circle", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "C", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "I", "rotation": 90}, "FRONT": {"patternId": "6", "rotation": 270}, "RIGHT": {"patternId": "4", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 0}, "LEFT": {"patternId": "C", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "4", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C335/initial_net.png", "targetTopFaceImage": "../images/C335/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 2, "targetRotationOffset": 90, "levelId": 335, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-335.json"}, "rollSequence": ["S", "W", "W", "S", "E", "S", "W", "S"], "observedPathFaces": [{"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "W", "S", "E", "S", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "I", "rotation": 90}, "FRONT": {"patternId": "6", "rotation": 270}, "RIGHT": {"patternId": "4", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 0}, "LEFT": {"patternId": "C", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C335\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=4, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=circle, rotation=0]\n[LEFT: patternId=C, rotation=90] [TOP: patternId=I, rotation=90] [RIGHT: patternId=4, rotation=0]\n [FRONT: patternId=6, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=circle, rotation=0\n- LEFT: patternId=C, rotation=90\n- TOP: patternId=I, rotation=90\n- RIGHT: patternId=4, rotation=0\n- FRONT: patternId=6, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C335/initial_net.png", "targetTopFaceImage": "images/C335/target_top_face.png"}, "__sample_id__": "C335"} +{"taskType": "roll_to_target_top_face", "code": "C336", "name": "Goal Roll C336", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "C", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "4", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "circle", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "3", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "D", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "L", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "C", "rotation": 180}, "FRONT": {"patternId": "4", "rotation": 270}, "RIGHT": {"patternId": "circle", "rotation": 270}, "BACK": {"patternId": "3", "rotation": 90}, "LEFT": {"patternId": "D", "rotation": 0}, "BOTTOM": {"patternId": "L", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "C", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C336/initial_net.png", "targetTopFaceImage": "../images/C336/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 6, "targetRotationOffset": 180, "levelId": 336, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-336.json"}, "rollSequence": ["S", "S", "W", "N", "N", "W", "N", "E"], "observedPathFaces": [{"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "W", "N", "N", "W", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "C", "rotation": 180}, "FRONT": {"patternId": "4", "rotation": 270}, "RIGHT": {"patternId": "circle", "rotation": 270}, "BACK": {"patternId": "3", "rotation": 90}, "LEFT": {"patternId": "D", "rotation": 0}, "BOTTOM": {"patternId": "L", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C336\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=C, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=3, rotation=90]\n[LEFT: patternId=D, rotation=0] [TOP: patternId=C, rotation=180] [RIGHT: patternId=circle, rotation=270]\n [FRONT: patternId=4, rotation=270]\n [BOTTOM: patternId=L, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=3, rotation=90\n- LEFT: patternId=D, rotation=0\n- TOP: patternId=C, rotation=180\n- RIGHT: patternId=circle, rotation=270\n- FRONT: patternId=4, rotation=270\n- BOTTOM: patternId=L, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C336/initial_net.png", "targetTopFaceImage": "images/C336/target_top_face.png"}, "__sample_id__": "C336"} +{"taskType": "roll_to_target_top_face", "code": "C337", "name": "Goal Roll C337", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "plus", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "6", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "O", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "triangle", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "K", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "plus", "rotation": 270}, "FRONT": {"patternId": "6", "rotation": 270}, "RIGHT": {"patternId": "O", "rotation": 90}, "BACK": {"patternId": "triangle", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "K", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "K", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C337/initial_net.png", "targetTopFaceImage": "../images/C337/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 6, "targetRotationOffset": 180, "levelId": 337, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-337.json"}, "rollSequence": ["S", "E", "W", "E", "W", "S", "S", "S"], "observedPathFaces": [{"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "W", "E", "W", "S", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "plus", "rotation": 270}, "FRONT": {"patternId": "6", "rotation": 270}, "RIGHT": {"patternId": "O", "rotation": 90}, "BACK": {"patternId": "triangle", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "K", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C337\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=K, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=triangle, rotation=270]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=plus, rotation=270] [RIGHT: patternId=O, rotation=90]\n [FRONT: patternId=6, rotation=270]\n [BOTTOM: patternId=K, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=triangle, rotation=270\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=plus, rotation=270\n- RIGHT: patternId=O, rotation=90\n- FRONT: patternId=6, rotation=270\n- BOTTOM: patternId=K, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C337/initial_net.png", "targetTopFaceImage": "images/C337/target_top_face.png"}, "__sample_id__": "C337"} +{"taskType": "roll_to_target_top_face", "code": "C338", "name": "Goal Roll C338", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "4", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "L", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "5", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "I", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "8", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "H", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "4", "rotation": 0}, "FRONT": {"patternId": "L", "rotation": 270}, "RIGHT": {"patternId": "5", "rotation": 180}, "BACK": {"patternId": "I", "rotation": 270}, "LEFT": {"patternId": "8", "rotation": 0}, "BOTTOM": {"patternId": "H", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "4", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C338/initial_net.png", "targetTopFaceImage": "../images/C338/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 5, "targetRotationOffset": 180, "levelId": 338, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-338.json"}, "rollSequence": ["W", "W", "W", "N", "W", "W", "W", "N"], "observedPathFaces": [{"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "W", "N", "W", "W", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "4", "rotation": 0}, "FRONT": {"patternId": "L", "rotation": 270}, "RIGHT": {"patternId": "5", "rotation": 180}, "BACK": {"patternId": "I", "rotation": 270}, "LEFT": {"patternId": "8", "rotation": 0}, "BOTTOM": {"patternId": "H", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C338\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=4, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=I, rotation=270]\n[LEFT: patternId=8, rotation=0] [TOP: patternId=4, rotation=0] [RIGHT: patternId=5, rotation=180]\n [FRONT: patternId=L, rotation=270]\n [BOTTOM: patternId=H, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=I, rotation=270\n- LEFT: patternId=8, rotation=0\n- TOP: patternId=4, rotation=0\n- RIGHT: patternId=5, rotation=180\n- FRONT: patternId=L, rotation=270\n- BOTTOM: patternId=H, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C338/initial_net.png", "targetTopFaceImage": "images/C338/target_top_face.png"}, "__sample_id__": "C338"} +{"taskType": "roll_to_target_top_face", "code": "C339", "name": "Goal Roll C339", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "N", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "D", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "A", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "smile", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "F", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "U", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "N", "rotation": 180}, "FRONT": {"patternId": "D", "rotation": 90}, "RIGHT": {"patternId": "A", "rotation": 270}, "BACK": {"patternId": "smile", "rotation": 180}, "LEFT": {"patternId": "F", "rotation": 0}, "BOTTOM": {"patternId": "U", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 7, "stepNumber": 8, "patternId": "smile", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C339/initial_net.png", "targetTopFaceImage": "../images/C339/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 8, "targetRotationOffset": 90, "levelId": 339, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-339.json"}, "rollSequence": ["W", "N", "E", "N", "E", "N", "E", "S"], "observedPathFaces": [{"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "E", "N", "E", "N", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "N", "rotation": 180}, "FRONT": {"patternId": "D", "rotation": 90}, "RIGHT": {"patternId": "A", "rotation": 270}, "BACK": {"patternId": "smile", "rotation": 180}, "LEFT": {"patternId": "F", "rotation": 0}, "BOTTOM": {"patternId": "U", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C339\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=smile, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=smile, rotation=180]\n[LEFT: patternId=F, rotation=0] [TOP: patternId=N, rotation=180] [RIGHT: patternId=A, rotation=270]\n [FRONT: patternId=D, rotation=90]\n [BOTTOM: patternId=U, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=smile, rotation=180\n- LEFT: patternId=F, rotation=0\n- TOP: patternId=N, rotation=180\n- RIGHT: patternId=A, rotation=270\n- FRONT: patternId=D, rotation=90\n- BOTTOM: patternId=U, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C339/initial_net.png", "targetTopFaceImage": "images/C339/target_top_face.png"}, "__sample_id__": "C339"} +{"taskType": "roll_to_target_top_face", "code": "C340", "name": "Goal Roll C340", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "U", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "V", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_right", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "F", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "A", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "U", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "V", "rotation": 180}, "BACK": {"patternId": "arrow_right", "rotation": 180}, "LEFT": {"patternId": "F", "rotation": 90}, "BOTTOM": {"patternId": "A", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "A", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C340/initial_net.png", "targetTopFaceImage": "../images/C340/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 2, "targetRotationOffset": 180, "levelId": 340, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-340.json"}, "rollSequence": ["E", "E", "W", "N", "W", "N", "E", "E"], "observedPathFaces": [{"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "W", "N", "W", "N", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "U", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "V", "rotation": 180}, "BACK": {"patternId": "arrow_right", "rotation": 180}, "LEFT": {"patternId": "F", "rotation": 90}, "BOTTOM": {"patternId": "A", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C340\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=A, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_right, rotation=180]\n[LEFT: patternId=F, rotation=90] [TOP: patternId=U, rotation=180] [RIGHT: patternId=V, rotation=180]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=A, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_right, rotation=180\n- LEFT: patternId=F, rotation=90\n- TOP: patternId=U, rotation=180\n- RIGHT: patternId=V, rotation=180\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=A, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C340/initial_net.png", "targetTopFaceImage": "images/C340/target_top_face.png"}, "__sample_id__": "C340"} +{"taskType": "roll_to_target_top_face", "code": "C341", "name": "Goal Roll C341", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "6", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "2", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "B", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "4", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "smile", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "D", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "6", "rotation": 270}, "FRONT": {"patternId": "2", "rotation": 270}, "RIGHT": {"patternId": "B", "rotation": 180}, "BACK": {"patternId": "4", "rotation": 270}, "LEFT": {"patternId": "smile", "rotation": 180}, "BOTTOM": {"patternId": "D", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 8, "stepNumber": 9, "patternId": "smile", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C341/initial_net.png", "targetTopFaceImage": "../images/C341/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 9, "targetRotationOffset": 90, "levelId": 341, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-341.json"}, "rollSequence": ["E", "W", "N", "W", "S", "W", "W", "W", "S"], "observedPathFaces": [{"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "W", "N", "W", "S", "W", "W", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "6", "rotation": 270}, "FRONT": {"patternId": "2", "rotation": 270}, "RIGHT": {"patternId": "B", "rotation": 180}, "BACK": {"patternId": "4", "rotation": 270}, "LEFT": {"patternId": "smile", "rotation": 180}, "BOTTOM": {"patternId": "D", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C341\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=smile, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=4, rotation=270]\n[LEFT: patternId=smile, rotation=180] [TOP: patternId=6, rotation=270] [RIGHT: patternId=B, rotation=180]\n [FRONT: patternId=2, rotation=270]\n [BOTTOM: patternId=D, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=4, rotation=270\n- LEFT: patternId=smile, rotation=180\n- TOP: patternId=6, rotation=270\n- RIGHT: patternId=B, rotation=180\n- FRONT: patternId=2, rotation=270\n- BOTTOM: patternId=D, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C341/initial_net.png", "targetTopFaceImage": "images/C341/target_top_face.png"}, "__sample_id__": "C341"} +{"taskType": "roll_to_target_top_face", "code": "C342", "name": "Goal Roll C342", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "circle", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "1", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "1", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "square", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "circle", "rotation": 90}, "FRONT": {"patternId": "1", "rotation": 180}, "RIGHT": {"patternId": "1", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "square", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 7, "stepNumber": 8, "patternId": "circle", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C342/initial_net.png", "targetTopFaceImage": "../images/C342/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 8, "targetRotationOffset": 270, "levelId": 342, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-342.json"}, "rollSequence": ["S", "S", "E", "E", "N", "N", "S", "S"], "observedPathFaces": [{"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "E", "E", "N", "N", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "circle", "rotation": 90}, "FRONT": {"patternId": "1", "rotation": 180}, "RIGHT": {"patternId": "1", "rotation": 180}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "square", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C342\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=circle, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=circle, rotation=90] [RIGHT: patternId=1, rotation=180]\n [FRONT: patternId=1, rotation=180]\n [BOTTOM: patternId=square, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=circle, rotation=90\n- RIGHT: patternId=1, rotation=180\n- FRONT: patternId=1, rotation=180\n- BOTTOM: patternId=square, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C342/initial_net.png", "targetTopFaceImage": "images/C342/target_top_face.png"}, "__sample_id__": "C342"} +{"taskType": "roll_to_target_top_face", "code": "C343", "name": "Goal Roll C343", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "6", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "6", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "F", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "J", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "L", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "J", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "6", "rotation": 180}, "FRONT": {"patternId": "6", "rotation": 90}, "RIGHT": {"patternId": "F", "rotation": 180}, "BACK": {"patternId": "J", "rotation": 0}, "LEFT": {"patternId": "L", "rotation": 90}, "BOTTOM": {"patternId": "J", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 6, "stepNumber": 7, "patternId": "F", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C343/initial_net.png", "targetTopFaceImage": "../images/C343/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 7, "targetRotationOffset": 180, "levelId": 343, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-343.json"}, "rollSequence": ["N", "W", "S", "S", "W", "S", "W", "W", "N"], "observedPathFaces": [{"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "S", "S", "W", "S", "W", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "6", "rotation": 180}, "FRONT": {"patternId": "6", "rotation": 90}, "RIGHT": {"patternId": "F", "rotation": 180}, "BACK": {"patternId": "J", "rotation": 0}, "LEFT": {"patternId": "L", "rotation": 90}, "BOTTOM": {"patternId": "J", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C343\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=F, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=J, rotation=0]\n[LEFT: patternId=L, rotation=90] [TOP: patternId=6, rotation=180] [RIGHT: patternId=F, rotation=180]\n [FRONT: patternId=6, rotation=90]\n [BOTTOM: patternId=J, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=J, rotation=0\n- LEFT: patternId=L, rotation=90\n- TOP: patternId=6, rotation=180\n- RIGHT: patternId=F, rotation=180\n- FRONT: patternId=6, rotation=90\n- BOTTOM: patternId=J, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C343/initial_net.png", "targetTopFaceImage": "images/C343/target_top_face.png"}, "__sample_id__": "C343"} +{"taskType": "roll_to_target_top_face", "code": "C344", "name": "Goal Roll C344", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "diamond", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_left", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_down", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "plus", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "P", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "diamond", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_left", "rotation": 270}, "BACK": {"patternId": "arrow_down", "rotation": 90}, "LEFT": {"patternId": "plus", "rotation": 180}, "BOTTOM": {"patternId": "P", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "plus", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C344/initial_net.png", "targetTopFaceImage": "../images/C344/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 3, "targetRotationOffset": 180, "levelId": 344, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-344.json"}, "rollSequence": ["N", "N", "E", "E", "S", "E", "N", "W"], "observedPathFaces": [{"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "E", "E", "S", "E", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "diamond", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_left", "rotation": 270}, "BACK": {"patternId": "arrow_down", "rotation": 90}, "LEFT": {"patternId": "plus", "rotation": 180}, "BOTTOM": {"patternId": "P", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C344\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=plus, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_down, rotation=90]\n[LEFT: patternId=plus, rotation=180] [TOP: patternId=diamond, rotation=0] [RIGHT: patternId=arrow_left, rotation=270]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=P, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_down, rotation=90\n- LEFT: patternId=plus, rotation=180\n- TOP: patternId=diamond, rotation=0\n- RIGHT: patternId=arrow_left, rotation=270\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=P, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C344/initial_net.png", "targetTopFaceImage": "images/C344/target_top_face.png"}, "__sample_id__": "C344"} +{"taskType": "roll_to_target_top_face", "code": "C345", "name": "Goal Roll C345", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "E", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "heart", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_left", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "4", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "heart", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "circle", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "E", "rotation": 270}, "FRONT": {"patternId": "heart", "rotation": 0}, "RIGHT": {"patternId": "arrow_left", "rotation": 270}, "BACK": {"patternId": "4", "rotation": 90}, "LEFT": {"patternId": "heart", "rotation": 0}, "BOTTOM": {"patternId": "circle", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 8, "stepNumber": 9, "patternId": "E", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C345/initial_net.png", "targetTopFaceImage": "../images/C345/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 9, "targetRotationOffset": 270, "levelId": 345, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-345.json"}, "rollSequence": ["W", "W", "N", "W", "S", "E", "N", "N", "E"], "observedPathFaces": [{"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "N", "W", "S", "E", "N", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "E", "rotation": 270}, "FRONT": {"patternId": "heart", "rotation": 0}, "RIGHT": {"patternId": "arrow_left", "rotation": 270}, "BACK": {"patternId": "4", "rotation": 90}, "LEFT": {"patternId": "heart", "rotation": 0}, "BOTTOM": {"patternId": "circle", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C345\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=E, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=4, rotation=90]\n[LEFT: patternId=heart, rotation=0] [TOP: patternId=E, rotation=270] [RIGHT: patternId=arrow_left, rotation=270]\n [FRONT: patternId=heart, rotation=0]\n [BOTTOM: patternId=circle, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=4, rotation=90\n- LEFT: patternId=heart, rotation=0\n- TOP: patternId=E, rotation=270\n- RIGHT: patternId=arrow_left, rotation=270\n- FRONT: patternId=heart, rotation=0\n- BOTTOM: patternId=circle, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C345/initial_net.png", "targetTopFaceImage": "images/C345/target_top_face.png"}, "__sample_id__": "C345"} +{"taskType": "roll_to_target_top_face", "code": "C346", "name": "Goal Roll C346", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "B", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "diamond", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "3", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "4", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "F", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "B", "rotation": 270}, "FRONT": {"patternId": "diamond", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "3", "rotation": 270}, "LEFT": {"patternId": "4", "rotation": 0}, "BOTTOM": {"patternId": "F", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "F", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C346/initial_net.png", "targetTopFaceImage": "../images/C346/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 2, "targetRotationOffset": 180, "levelId": 346, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-346.json"}, "rollSequence": ["S", "S", "N", "N", "N", "W", "N", "E", "E"], "observedPathFaces": [{"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "N", "N", "N", "W", "N", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "B", "rotation": 270}, "FRONT": {"patternId": "diamond", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "3", "rotation": 270}, "LEFT": {"patternId": "4", "rotation": 0}, "BOTTOM": {"patternId": "F", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C346\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=F, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=3, rotation=270]\n[LEFT: patternId=4, rotation=0] [TOP: patternId=B, rotation=270] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=diamond, rotation=270]\n [BOTTOM: patternId=F, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=3, rotation=270\n- LEFT: patternId=4, rotation=0\n- TOP: patternId=B, rotation=270\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=diamond, rotation=270\n- BOTTOM: patternId=F, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C346/initial_net.png", "targetTopFaceImage": "images/C346/target_top_face.png"}, "__sample_id__": "C346"} +{"taskType": "roll_to_target_top_face", "code": "C347", "name": "Goal Roll C347", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "S", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "2", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "T", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_right", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "S", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "2", "rotation": 180}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_right", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "arrow_right", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C347/initial_net.png", "targetTopFaceImage": "../images/C347/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 3, "targetRotationOffset": 270, "levelId": 347, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-347.json"}, "rollSequence": ["E", "N", "E", "S", "W", "N", "S", "E", "S"], "observedPathFaces": [{"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "E", "S", "W", "N", "S", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "S", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "2", "rotation": 180}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_right", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C347\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=arrow_right, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=T, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=S, rotation=90] [RIGHT: patternId=2, rotation=180]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=arrow_right, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=T, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=S, rotation=90\n- RIGHT: patternId=2, rotation=180\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=arrow_right, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C347/initial_net.png", "targetTopFaceImage": "images/C347/target_top_face.png"}, "__sample_id__": "C347"} +{"taskType": "roll_to_target_top_face", "code": "C348", "name": "Goal Roll C348", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "7", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "2", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "3", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "W", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "P", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "W", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "7", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 270}, "RIGHT": {"patternId": "3", "rotation": 270}, "BACK": {"patternId": "W", "rotation": 0}, "LEFT": {"patternId": "P", "rotation": 0}, "BOTTOM": {"patternId": "W", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "P", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C348/initial_net.png", "targetTopFaceImage": "../images/C348/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 2, "targetRotationOffset": 90, "levelId": 348, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-348.json"}, "rollSequence": ["N", "E", "E", "S", "S", "S", "E", "W"], "observedPathFaces": [{"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "E", "S", "S", "S", "E", "W"]}, "legacy_answer": {"TOP": {"patternId": "7", "rotation": 0}, "FRONT": {"patternId": "2", "rotation": 270}, "RIGHT": {"patternId": "3", "rotation": 270}, "BACK": {"patternId": "W", "rotation": 0}, "LEFT": {"patternId": "P", "rotation": 0}, "BOTTOM": {"patternId": "W", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C348\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=P, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=W, rotation=0]\n[LEFT: patternId=P, rotation=0] [TOP: patternId=7, rotation=0] [RIGHT: patternId=3, rotation=270]\n [FRONT: patternId=2, rotation=270]\n [BOTTOM: patternId=W, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=W, rotation=0\n- LEFT: patternId=P, rotation=0\n- TOP: patternId=7, rotation=0\n- RIGHT: patternId=3, rotation=270\n- FRONT: patternId=2, rotation=270\n- BOTTOM: patternId=W, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C348/initial_net.png", "targetTopFaceImage": "images/C348/target_top_face.png"}, "__sample_id__": "C348"} +{"taskType": "roll_to_target_top_face", "code": "C349", "name": "Goal Roll C349", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "plus", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "G", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Q", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_up", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "G", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_up", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "plus", "rotation": 0}, "FRONT": {"patternId": "G", "rotation": 180}, "RIGHT": {"patternId": "Q", "rotation": 180}, "BACK": {"patternId": "arrow_up", "rotation": 0}, "LEFT": {"patternId": "G", "rotation": 90}, "BOTTOM": {"patternId": "arrow_up", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "arrow_up", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C349/initial_net.png", "targetTopFaceImage": "../images/C349/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 349, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-349.json"}, "rollSequence": ["S", "W", "N", "W", "E", "N", "W", "N", "W"], "observedPathFaces": [{"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "N", "W", "E", "N", "W", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "plus", "rotation": 0}, "FRONT": {"patternId": "G", "rotation": 180}, "RIGHT": {"patternId": "Q", "rotation": 180}, "BACK": {"patternId": "arrow_up", "rotation": 0}, "LEFT": {"patternId": "G", "rotation": 90}, "BOTTOM": {"patternId": "arrow_up", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C349\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=arrow_up, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_up, rotation=0]\n[LEFT: patternId=G, rotation=90] [TOP: patternId=plus, rotation=0] [RIGHT: patternId=Q, rotation=180]\n [FRONT: patternId=G, rotation=180]\n [BOTTOM: patternId=arrow_up, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_up, rotation=0\n- LEFT: patternId=G, rotation=90\n- TOP: patternId=plus, rotation=0\n- RIGHT: patternId=Q, rotation=180\n- FRONT: patternId=G, rotation=180\n- BOTTOM: patternId=arrow_up, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C349/initial_net.png", "targetTopFaceImage": "images/C349/target_top_face.png"}, "__sample_id__": "C349"} +{"taskType": "roll_to_target_top_face", "code": "C350", "name": "Goal Roll C350", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "R", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "N", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "P", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "H", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "V", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_up", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "R", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 90}, "RIGHT": {"patternId": "P", "rotation": 0}, "BACK": {"patternId": "H", "rotation": 0}, "LEFT": {"patternId": "V", "rotation": 90}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "P", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C350/initial_net.png", "targetTopFaceImage": "../images/C350/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 4, "targetRotationOffset": 180, "levelId": 350, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-350.json"}, "rollSequence": ["S", "E", "S", "S", "W", "S", "S", "W", "W"], "observedPathFaces": [{"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "S", "S", "W", "S", "S", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "R", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 90}, "RIGHT": {"patternId": "P", "rotation": 0}, "BACK": {"patternId": "H", "rotation": 0}, "LEFT": {"patternId": "V", "rotation": 90}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C350\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=P, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=H, rotation=0]\n[LEFT: patternId=V, rotation=90] [TOP: patternId=R, rotation=0] [RIGHT: patternId=P, rotation=0]\n [FRONT: patternId=N, rotation=90]\n [BOTTOM: patternId=arrow_up, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=H, rotation=0\n- LEFT: patternId=V, rotation=90\n- TOP: patternId=R, rotation=0\n- RIGHT: patternId=P, rotation=0\n- FRONT: patternId=N, rotation=90\n- BOTTOM: patternId=arrow_up, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C350/initial_net.png", "targetTopFaceImage": "images/C350/target_top_face.png"}, "__sample_id__": "C350"} +{"taskType": "roll_to_target_top_face", "code": "C351", "name": "Goal Roll C351", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "smile", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "F", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "7", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "E", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "smile", "rotation": 180}, "FRONT": {"patternId": "F", "rotation": 90}, "RIGHT": {"patternId": "7", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "E", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 7, "stepNumber": 8, "patternId": "E", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C351/initial_net.png", "targetTopFaceImage": "../images/C351/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 8, "targetRotationOffset": 180, "levelId": 351, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-351.json"}, "rollSequence": ["E", "S", "E", "N", "W", "N", "E", "E"], "observedPathFaces": [{"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "E", "N", "W", "N", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "smile", "rotation": 180}, "FRONT": {"patternId": "F", "rotation": 90}, "RIGHT": {"patternId": "7", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "E", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C351\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=E, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=smile, rotation=180] [RIGHT: patternId=7, rotation=0]\n [FRONT: patternId=F, rotation=90]\n [BOTTOM: patternId=E, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=smile, rotation=180\n- RIGHT: patternId=7, rotation=0\n- FRONT: patternId=F, rotation=90\n- BOTTOM: patternId=E, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C351/initial_net.png", "targetTopFaceImage": "images/C351/target_top_face.png"}, "__sample_id__": "C351"} +{"taskType": "roll_to_target_top_face", "code": "C352", "name": "Goal Roll C352", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "S", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "V", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "K", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "U", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "7", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "N", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "S", "rotation": 180}, "FRONT": {"patternId": "V", "rotation": 180}, "RIGHT": {"patternId": "K", "rotation": 0}, "BACK": {"patternId": "U", "rotation": 270}, "LEFT": {"patternId": "7", "rotation": 90}, "BOTTOM": {"patternId": "N", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "N", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C352/initial_net.png", "targetTopFaceImage": "../images/C352/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 3, "targetRotationOffset": 90, "levelId": 352, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-352.json"}, "rollSequence": ["W", "S", "W", "N", "E", "E", "S", "E", "E"], "observedPathFaces": [{"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "W", "N", "E", "E", "S", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "S", "rotation": 180}, "FRONT": {"patternId": "V", "rotation": 180}, "RIGHT": {"patternId": "K", "rotation": 0}, "BACK": {"patternId": "U", "rotation": 270}, "LEFT": {"patternId": "7", "rotation": 90}, "BOTTOM": {"patternId": "N", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C352\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=N, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=U, rotation=270]\n[LEFT: patternId=7, rotation=90] [TOP: patternId=S, rotation=180] [RIGHT: patternId=K, rotation=0]\n [FRONT: patternId=V, rotation=180]\n [BOTTOM: patternId=N, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=U, rotation=270\n- LEFT: patternId=7, rotation=90\n- TOP: patternId=S, rotation=180\n- RIGHT: patternId=K, rotation=0\n- FRONT: patternId=V, rotation=180\n- BOTTOM: patternId=N, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C352/initial_net.png", "targetTopFaceImage": "images/C352/target_top_face.png"}, "__sample_id__": "C352"} +{"taskType": "roll_to_target_top_face", "code": "C353", "name": "Goal Roll C353", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "G", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "C", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "J", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "square", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "T", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "G", "rotation": 0}, "FRONT": {"patternId": "C", "rotation": 90}, "RIGHT": {"patternId": "J", "rotation": 90}, "BACK": {"patternId": "square", "rotation": 180}, "LEFT": {"patternId": "T", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "J", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C353/initial_net.png", "targetTopFaceImage": "../images/C353/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 5, "targetRotationOffset": 180, "levelId": 353, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-353.json"}, "rollSequence": ["S", "S", "W", "E", "W", "S", "E", "S", "E"], "observedPathFaces": [{"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "W", "E", "W", "S", "E", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "G", "rotation": 0}, "FRONT": {"patternId": "C", "rotation": 90}, "RIGHT": {"patternId": "J", "rotation": 90}, "BACK": {"patternId": "square", "rotation": 180}, "LEFT": {"patternId": "T", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C353\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=J, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=square, rotation=180]\n[LEFT: patternId=T, rotation=180] [TOP: patternId=G, rotation=0] [RIGHT: patternId=J, rotation=90]\n [FRONT: patternId=C, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=square, rotation=180\n- LEFT: patternId=T, rotation=180\n- TOP: patternId=G, rotation=0\n- RIGHT: patternId=J, rotation=90\n- FRONT: patternId=C, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C353/initial_net.png", "targetTopFaceImage": "images/C353/target_top_face.png"}, "__sample_id__": "C353"} +{"taskType": "roll_to_target_top_face", "code": "C354", "name": "Goal Roll C354", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "star", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "6", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_down", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "P", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "A", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "star", "rotation": 90}, "RIGHT": {"patternId": "6", "rotation": 90}, "BACK": {"patternId": "arrow_down", "rotation": 180}, "LEFT": {"patternId": "P", "rotation": 180}, "BOTTOM": {"patternId": "A", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "star", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C354/initial_net.png", "targetTopFaceImage": "../images/C354/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 4, "targetRotationOffset": 90, "levelId": 354, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-354.json"}, "rollSequence": ["E", "S", "S", "S", "W", "S", "W", "N"], "observedPathFaces": [{"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "S", "S", "W", "S", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "star", "rotation": 90}, "RIGHT": {"patternId": "6", "rotation": 90}, "BACK": {"patternId": "arrow_down", "rotation": 180}, "LEFT": {"patternId": "P", "rotation": 180}, "BOTTOM": {"patternId": "A", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C354\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=star, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_down, rotation=180]\n[LEFT: patternId=P, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=6, rotation=90]\n [FRONT: patternId=star, rotation=90]\n [BOTTOM: patternId=A, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_down, rotation=180\n- LEFT: patternId=P, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=6, rotation=90\n- FRONT: patternId=star, rotation=90\n- BOTTOM: patternId=A, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C354/initial_net.png", "targetTopFaceImage": "images/C354/target_top_face.png"}, "__sample_id__": "C354"} +{"taskType": "roll_to_target_top_face", "code": "C355", "name": "Goal Roll C355", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "A", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "2", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "Y", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "X", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "smile", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "A", "rotation": 180}, "RIGHT": {"patternId": "2", "rotation": 0}, "BACK": {"patternId": "Y", "rotation": 0}, "LEFT": {"patternId": "X", "rotation": 90}, "BOTTOM": {"patternId": "smile", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 8, "stepNumber": 9, "patternId": "2", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C355/initial_net.png", "targetTopFaceImage": "../images/C355/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 9, "targetRotationOffset": 180, "levelId": 355, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-355.json"}, "rollSequence": ["N", "S", "S", "E", "N", "W", "N", "N", "S"], "observedPathFaces": [{"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "S", "S", "E", "N", "W", "N", "N", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "A", "rotation": 180}, "RIGHT": {"patternId": "2", "rotation": 0}, "BACK": {"patternId": "Y", "rotation": 0}, "LEFT": {"patternId": "X", "rotation": 90}, "BOTTOM": {"patternId": "smile", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C355\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=2, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=Y, rotation=0]\n[LEFT: patternId=X, rotation=90] [TOP: patternId=?, rotation=0] [RIGHT: patternId=2, rotation=0]\n [FRONT: patternId=A, rotation=180]\n [BOTTOM: patternId=smile, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Y, rotation=0\n- LEFT: patternId=X, rotation=90\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=2, rotation=0\n- FRONT: patternId=A, rotation=180\n- BOTTOM: patternId=smile, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C355/initial_net.png", "targetTopFaceImage": "images/C355/target_top_face.png"}, "__sample_id__": "C355"} +{"taskType": "roll_to_target_top_face", "code": "C356", "name": "Goal Roll C356", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "Z", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "X", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_left", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "star", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "Z", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "Z", "rotation": 270}, "FRONT": {"patternId": "X", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 270}, "LEFT": {"patternId": "star", "rotation": 180}, "BOTTOM": {"patternId": "Z", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "Z", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C356/initial_net.png", "targetTopFaceImage": "../images/C356/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 5, "targetRotationOffset": 180, "levelId": 356, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-356.json"}, "rollSequence": ["S", "S", "S", "W", "S", "W", "N", "N", "E"], "observedPathFaces": [{"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "S", "W", "S", "W", "N", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "Z", "rotation": 270}, "FRONT": {"patternId": "X", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 270}, "LEFT": {"patternId": "star", "rotation": 180}, "BOTTOM": {"patternId": "Z", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C356\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=Z, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_left, rotation=270]\n[LEFT: patternId=star, rotation=180] [TOP: patternId=Z, rotation=270] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=X, rotation=0]\n [BOTTOM: patternId=Z, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_left, rotation=270\n- LEFT: patternId=star, rotation=180\n- TOP: patternId=Z, rotation=270\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=X, rotation=0\n- BOTTOM: patternId=Z, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C356/initial_net.png", "targetTopFaceImage": "images/C356/target_top_face.png"}, "__sample_id__": "C356"} +{"taskType": "roll_to_target_top_face", "code": "C357", "name": "Goal Roll C357", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "D", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "W", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "7", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "Z", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 180}, "RIGHT": {"patternId": "W", "rotation": 180}, "BACK": {"patternId": "7", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "Z", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "7", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C357/initial_net.png", "targetTopFaceImage": "../images/C357/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 357, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-357.json"}, "rollSequence": ["S", "E", "E", "N", "W", "N", "E", "W"], "observedPathFaces": [{"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "E", "N", "W", "N", "E", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "D", "rotation": 180}, "RIGHT": {"patternId": "W", "rotation": 180}, "BACK": {"patternId": "7", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "Z", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C357\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=7, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=7, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=W, rotation=180]\n [FRONT: patternId=D, rotation=180]\n [BOTTOM: patternId=Z, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=7, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=W, rotation=180\n- FRONT: patternId=D, rotation=180\n- BOTTOM: patternId=Z, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C357/initial_net.png", "targetTopFaceImage": "images/C357/target_top_face.png"}, "__sample_id__": "C357"} +{"taskType": "roll_to_target_top_face", "code": "C358", "name": "Goal Roll C358", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "B", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "V", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "5", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "M", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "Z", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "I", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "B", "rotation": 90}, "FRONT": {"patternId": "V", "rotation": 270}, "RIGHT": {"patternId": "5", "rotation": 90}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "Z", "rotation": 90}, "BOTTOM": {"patternId": "I", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "Z", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C358/initial_net.png", "targetTopFaceImage": "../images/C358/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 2, "targetRotationOffset": 180, "levelId": 358, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-358.json"}, "rollSequence": ["N", "E", "E", "N", "E", "S", "S", "E"], "observedPathFaces": [{"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "E", "N", "E", "S", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "B", "rotation": 90}, "FRONT": {"patternId": "V", "rotation": 270}, "RIGHT": {"patternId": "5", "rotation": 90}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "Z", "rotation": 90}, "BOTTOM": {"patternId": "I", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C358\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=Z, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=M, rotation=0]\n[LEFT: patternId=Z, rotation=90] [TOP: patternId=B, rotation=90] [RIGHT: patternId=5, rotation=90]\n [FRONT: patternId=V, rotation=270]\n [BOTTOM: patternId=I, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=M, rotation=0\n- LEFT: patternId=Z, rotation=90\n- TOP: patternId=B, rotation=90\n- RIGHT: patternId=5, rotation=90\n- FRONT: patternId=V, rotation=270\n- BOTTOM: patternId=I, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C358/initial_net.png", "targetTopFaceImage": "images/C358/target_top_face.png"}, "__sample_id__": "C358"} +{"taskType": "roll_to_target_top_face", "code": "C359", "name": "Goal Roll C359", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "B", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "G", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "F", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "P", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "circle", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "B", "rotation": 90}, "RIGHT": {"patternId": "G", "rotation": 90}, "BACK": {"patternId": "F", "rotation": 270}, "LEFT": {"patternId": "P", "rotation": 0}, "BOTTOM": {"patternId": "circle", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "B", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C359/initial_net.png", "targetTopFaceImage": "../images/C359/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 2, "targetRotationOffset": 180, "levelId": 359, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-359.json"}, "rollSequence": ["E", "N", "W", "N", "W", "S", "W", "N", "E"], "observedPathFaces": [{"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "W", "N", "W", "S", "W", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "B", "rotation": 90}, "RIGHT": {"patternId": "G", "rotation": 90}, "BACK": {"patternId": "F", "rotation": 270}, "LEFT": {"patternId": "P", "rotation": 0}, "BOTTOM": {"patternId": "circle", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C359\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=B, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=F, rotation=270]\n[LEFT: patternId=P, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=G, rotation=90]\n [FRONT: patternId=B, rotation=90]\n [BOTTOM: patternId=circle, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=F, rotation=270\n- LEFT: patternId=P, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=G, rotation=90\n- FRONT: patternId=B, rotation=90\n- BOTTOM: patternId=circle, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C359/initial_net.png", "targetTopFaceImage": "images/C359/target_top_face.png"}, "__sample_id__": "C359"} +{"taskType": "roll_to_target_top_face", "code": "C360", "name": "Goal Roll C360", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "X", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "K", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "H", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "smile", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "square", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "X", "rotation": 180}, "FRONT": {"patternId": "K", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "H", "rotation": 270}, "LEFT": {"patternId": "smile", "rotation": 0}, "BOTTOM": {"patternId": "square", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 7, "stepNumber": 8, "patternId": "X", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C360/initial_net.png", "targetTopFaceImage": "../images/C360/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 8, "targetRotationOffset": 90, "levelId": 360, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-360.json"}, "rollSequence": ["S", "W", "W", "S", "E", "S", "N", "E", "S"], "observedPathFaces": [{"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "W", "S", "E", "S", "N", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "X", "rotation": 180}, "FRONT": {"patternId": "K", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "H", "rotation": 270}, "LEFT": {"patternId": "smile", "rotation": 0}, "BOTTOM": {"patternId": "square", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C360\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=X, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=H, rotation=270]\n[LEFT: patternId=smile, rotation=0] [TOP: patternId=X, rotation=180] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=K, rotation=180]\n [BOTTOM: patternId=square, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=H, rotation=270\n- LEFT: patternId=smile, rotation=0\n- TOP: patternId=X, rotation=180\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=K, rotation=180\n- BOTTOM: patternId=square, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C360/initial_net.png", "targetTopFaceImage": "images/C360/target_top_face.png"}, "__sample_id__": "C360"} +{"taskType": "roll_to_target_top_face", "code": "C361", "name": "Goal Roll C361", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "T", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "triangle", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "T", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "6", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "circle", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "T", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "triangle", "rotation": 270}, "BACK": {"patternId": "T", "rotation": 90}, "LEFT": {"patternId": "6", "rotation": 0}, "BOTTOM": {"patternId": "circle", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 7, "stepNumber": 8, "patternId": "circle", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C361/initial_net.png", "targetTopFaceImage": "../images/C361/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 8, "targetRotationOffset": 180, "levelId": 361, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-361.json"}, "rollSequence": ["N", "E", "S", "S", "S", "N", "W", "S", "W"], "observedPathFaces": [{"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "S", "S", "S", "N", "W", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "T", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "triangle", "rotation": 270}, "BACK": {"patternId": "T", "rotation": 90}, "LEFT": {"patternId": "6", "rotation": 0}, "BOTTOM": {"patternId": "circle", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C361\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=circle, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=T, rotation=90]\n[LEFT: patternId=6, rotation=0] [TOP: patternId=T, rotation=270] [RIGHT: patternId=triangle, rotation=270]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=circle, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=T, rotation=90\n- LEFT: patternId=6, rotation=0\n- TOP: patternId=T, rotation=270\n- RIGHT: patternId=triangle, rotation=270\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=circle, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C361/initial_net.png", "targetTopFaceImage": "images/C361/target_top_face.png"}, "__sample_id__": "C361"} +{"taskType": "roll_to_target_top_face", "code": "C362", "name": "Goal Roll C362", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "Q", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "circle", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "G", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "triangle", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "W", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "Q", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "circle", "rotation": 90}, "BACK": {"patternId": "G", "rotation": 270}, "LEFT": {"patternId": "triangle", "rotation": 270}, "BOTTOM": {"patternId": "W", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "triangle", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C362/initial_net.png", "targetTopFaceImage": "../images/C362/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 5, "targetRotationOffset": 270, "levelId": 362, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-362.json"}, "rollSequence": ["W", "W", "N", "N", "W", "W", "S", "W"], "observedPathFaces": [{"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "N", "N", "W", "W", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "Q", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "circle", "rotation": 90}, "BACK": {"patternId": "G", "rotation": 270}, "LEFT": {"patternId": "triangle", "rotation": 270}, "BOTTOM": {"patternId": "W", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C362\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=triangle, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=G, rotation=270]\n[LEFT: patternId=triangle, rotation=270] [TOP: patternId=Q, rotation=180] [RIGHT: patternId=circle, rotation=90]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=W, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=G, rotation=270\n- LEFT: patternId=triangle, rotation=270\n- TOP: patternId=Q, rotation=180\n- RIGHT: patternId=circle, rotation=90\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=W, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C362/initial_net.png", "targetTopFaceImage": "images/C362/target_top_face.png"}, "__sample_id__": "C362"} +{"taskType": "roll_to_target_top_face", "code": "C363", "name": "Goal Roll C363", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "4", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "N", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Q", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "E", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "9", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "U", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "4", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 270}, "RIGHT": {"patternId": "Q", "rotation": 0}, "BACK": {"patternId": "E", "rotation": 90}, "LEFT": {"patternId": "9", "rotation": 180}, "BOTTOM": {"patternId": "U", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "9", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C363/initial_net.png", "targetTopFaceImage": "../images/C363/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 4, "targetRotationOffset": 180, "levelId": 363, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-363.json"}, "rollSequence": ["E", "N", "E", "S", "E", "E", "E", "S", "E"], "observedPathFaces": [{"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "E", "S", "E", "E", "E", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "4", "rotation": 0}, "FRONT": {"patternId": "N", "rotation": 270}, "RIGHT": {"patternId": "Q", "rotation": 0}, "BACK": {"patternId": "E", "rotation": 90}, "LEFT": {"patternId": "9", "rotation": 180}, "BOTTOM": {"patternId": "U", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C363\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=9, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=E, rotation=90]\n[LEFT: patternId=9, rotation=180] [TOP: patternId=4, rotation=0] [RIGHT: patternId=Q, rotation=0]\n [FRONT: patternId=N, rotation=270]\n [BOTTOM: patternId=U, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=E, rotation=90\n- LEFT: patternId=9, rotation=180\n- TOP: patternId=4, rotation=0\n- RIGHT: patternId=Q, rotation=0\n- FRONT: patternId=N, rotation=270\n- BOTTOM: patternId=U, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C363/initial_net.png", "targetTopFaceImage": "images/C363/target_top_face.png"}, "__sample_id__": "C363"} +{"taskType": "roll_to_target_top_face", "code": "C364", "name": "Goal Roll C364", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "arrow_left", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "arrow_down", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "plus", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "U", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "O", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "P", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "arrow_left", "rotation": 180}, "FRONT": {"patternId": "arrow_down", "rotation": 0}, "RIGHT": {"patternId": "plus", "rotation": 90}, "BACK": {"patternId": "U", "rotation": 180}, "LEFT": {"patternId": "O", "rotation": 180}, "BOTTOM": {"patternId": "P", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "U", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C364/initial_net.png", "targetTopFaceImage": "../images/C364/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 4, "targetRotationOffset": 90, "levelId": 364, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-364.json"}, "rollSequence": ["N", "W", "N", "W", "N", "W", "S", "E"], "observedPathFaces": [{"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "N", "W", "N", "W", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "arrow_left", "rotation": 180}, "FRONT": {"patternId": "arrow_down", "rotation": 0}, "RIGHT": {"patternId": "plus", "rotation": 90}, "BACK": {"patternId": "U", "rotation": 180}, "LEFT": {"patternId": "O", "rotation": 180}, "BOTTOM": {"patternId": "P", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C364\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=U, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=U, rotation=180]\n[LEFT: patternId=O, rotation=180] [TOP: patternId=arrow_left, rotation=180] [RIGHT: patternId=plus, rotation=90]\n [FRONT: patternId=arrow_down, rotation=0]\n [BOTTOM: patternId=P, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=U, rotation=180\n- LEFT: patternId=O, rotation=180\n- TOP: patternId=arrow_left, rotation=180\n- RIGHT: patternId=plus, rotation=90\n- FRONT: patternId=arrow_down, rotation=0\n- BOTTOM: patternId=P, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C364/initial_net.png", "targetTopFaceImage": "images/C364/target_top_face.png"}, "__sample_id__": "C364"} +{"taskType": "roll_to_target_top_face", "code": "C365", "name": "Goal Roll C365", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "S", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "W", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Q", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "plus", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "G", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "triangle", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "S", "rotation": 0}, "FRONT": {"patternId": "W", "rotation": 90}, "RIGHT": {"patternId": "Q", "rotation": 180}, "BACK": {"patternId": "plus", "rotation": 270}, "LEFT": {"patternId": "G", "rotation": 0}, "BOTTOM": {"patternId": "triangle", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "plus", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C365/initial_net.png", "targetTopFaceImage": "../images/C365/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 2, "targetRotationOffset": 180, "levelId": 365, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-365.json"}, "rollSequence": ["W", "S", "W", "W", "W", "N", "W", "N", "W"], "observedPathFaces": [{"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "W", "W", "W", "N", "W", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "S", "rotation": 0}, "FRONT": {"patternId": "W", "rotation": 90}, "RIGHT": {"patternId": "Q", "rotation": 180}, "BACK": {"patternId": "plus", "rotation": 270}, "LEFT": {"patternId": "G", "rotation": 0}, "BOTTOM": {"patternId": "triangle", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C365\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=plus, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=plus, rotation=270]\n[LEFT: patternId=G, rotation=0] [TOP: patternId=S, rotation=0] [RIGHT: patternId=Q, rotation=180]\n [FRONT: patternId=W, rotation=90]\n [BOTTOM: patternId=triangle, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=plus, rotation=270\n- LEFT: patternId=G, rotation=0\n- TOP: patternId=S, rotation=0\n- RIGHT: patternId=Q, rotation=180\n- FRONT: patternId=W, rotation=90\n- BOTTOM: patternId=triangle, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C365/initial_net.png", "targetTopFaceImage": "images/C365/target_top_face.png"}, "__sample_id__": "C365"} +{"taskType": "roll_to_target_top_face", "code": "C366", "name": "Goal Roll C366", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "I", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "2", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "6", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "K", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "J", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "F", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "I", "rotation": 90}, "FRONT": {"patternId": "2", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 90}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "J", "rotation": 0}, "BOTTOM": {"patternId": "F", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "6", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C366/initial_net.png", "targetTopFaceImage": "../images/C366/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 366, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-366.json"}, "rollSequence": ["W", "W", "N", "N", "E", "N", "N", "E", "S"], "observedPathFaces": [{"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "N", "N", "E", "N", "N", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "I", "rotation": 90}, "FRONT": {"patternId": "2", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 90}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "J", "rotation": 0}, "BOTTOM": {"patternId": "F", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C366\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=6, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=K, rotation=270]\n[LEFT: patternId=J, rotation=0] [TOP: patternId=I, rotation=90] [RIGHT: patternId=6, rotation=90]\n [FRONT: patternId=2, rotation=0]\n [BOTTOM: patternId=F, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=K, rotation=270\n- LEFT: patternId=J, rotation=0\n- TOP: patternId=I, rotation=90\n- RIGHT: patternId=6, rotation=90\n- FRONT: patternId=2, rotation=0\n- BOTTOM: patternId=F, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C366/initial_net.png", "targetTopFaceImage": "images/C366/target_top_face.png"}, "__sample_id__": "C366"} +{"taskType": "roll_to_target_top_face", "code": "C367", "name": "Goal Roll C367", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "star", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "2", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_right", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "T", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "G", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "1", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "star", "rotation": 90}, "FRONT": {"patternId": "2", "rotation": 180}, "RIGHT": {"patternId": "arrow_right", "rotation": 180}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "G", "rotation": 0}, "BOTTOM": {"patternId": "1", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "T", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C367/initial_net.png", "targetTopFaceImage": "../images/C367/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 367, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-367.json"}, "rollSequence": ["S", "N", "E", "N", "W", "N", "N", "E", "S"], "observedPathFaces": [{"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "N", "E", "N", "W", "N", "N", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "star", "rotation": 90}, "FRONT": {"patternId": "2", "rotation": 180}, "RIGHT": {"patternId": "arrow_right", "rotation": 180}, "BACK": {"patternId": "T", "rotation": 180}, "LEFT": {"patternId": "G", "rotation": 0}, "BOTTOM": {"patternId": "1", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C367\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=T, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=T, rotation=180]\n[LEFT: patternId=G, rotation=0] [TOP: patternId=star, rotation=90] [RIGHT: patternId=arrow_right, rotation=180]\n [FRONT: patternId=2, rotation=180]\n [BOTTOM: patternId=1, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=T, rotation=180\n- LEFT: patternId=G, rotation=0\n- TOP: patternId=star, rotation=90\n- RIGHT: patternId=arrow_right, rotation=180\n- FRONT: patternId=2, rotation=180\n- BOTTOM: patternId=1, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C367/initial_net.png", "targetTopFaceImage": "images/C367/target_top_face.png"}, "__sample_id__": "C367"} +{"taskType": "roll_to_target_top_face", "code": "C368", "name": "Goal Roll C368", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "4", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "O", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "plus", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "R", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "O", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_up", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "4", "rotation": 0}, "FRONT": {"patternId": "O", "rotation": 180}, "RIGHT": {"patternId": "plus", "rotation": 90}, "BACK": {"patternId": "R", "rotation": 270}, "LEFT": {"patternId": "O", "rotation": 90}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "R", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C368/initial_net.png", "targetTopFaceImage": "../images/C368/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 368, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-368.json"}, "rollSequence": ["S", "E", "N", "N", "E", "S", "E", "N", "E"], "observedPathFaces": [{"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "N", "N", "E", "S", "E", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "4", "rotation": 0}, "FRONT": {"patternId": "O", "rotation": 180}, "RIGHT": {"patternId": "plus", "rotation": 90}, "BACK": {"patternId": "R", "rotation": 270}, "LEFT": {"patternId": "O", "rotation": 90}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C368\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=R, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=R, rotation=270]\n[LEFT: patternId=O, rotation=90] [TOP: patternId=4, rotation=0] [RIGHT: patternId=plus, rotation=90]\n [FRONT: patternId=O, rotation=180]\n [BOTTOM: patternId=arrow_up, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=R, rotation=270\n- LEFT: patternId=O, rotation=90\n- TOP: patternId=4, rotation=0\n- RIGHT: patternId=plus, rotation=90\n- FRONT: patternId=O, rotation=180\n- BOTTOM: patternId=arrow_up, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C368/initial_net.png", "targetTopFaceImage": "images/C368/target_top_face.png"}, "__sample_id__": "C368"} +{"taskType": "roll_to_target_top_face", "code": "C369", "name": "Goal Roll C369", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "arrow_down", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "I", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "3", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "Q", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_down", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "2", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "arrow_down", "rotation": 0}, "FRONT": {"patternId": "I", "rotation": 90}, "RIGHT": {"patternId": "3", "rotation": 270}, "BACK": {"patternId": "Q", "rotation": 270}, "LEFT": {"patternId": "arrow_down", "rotation": 90}, "BOTTOM": {"patternId": "2", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 8, "stepNumber": 9, "patternId": "arrow_down", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C369/initial_net.png", "targetTopFaceImage": "../images/C369/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 9, "targetRotationOffset": 90, "levelId": 369, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-369.json"}, "rollSequence": ["S", "S", "W", "E", "E", "N", "W", "W", "W"], "observedPathFaces": [{"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "W", "E", "E", "N", "W", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "arrow_down", "rotation": 0}, "FRONT": {"patternId": "I", "rotation": 90}, "RIGHT": {"patternId": "3", "rotation": 270}, "BACK": {"patternId": "Q", "rotation": 270}, "LEFT": {"patternId": "arrow_down", "rotation": 90}, "BOTTOM": {"patternId": "2", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C369\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=arrow_down, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=Q, rotation=270]\n[LEFT: patternId=arrow_down, rotation=90] [TOP: patternId=arrow_down, rotation=0] [RIGHT: patternId=3, rotation=270]\n [FRONT: patternId=I, rotation=90]\n [BOTTOM: patternId=2, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Q, rotation=270\n- LEFT: patternId=arrow_down, rotation=90\n- TOP: patternId=arrow_down, rotation=0\n- RIGHT: patternId=3, rotation=270\n- FRONT: patternId=I, rotation=90\n- BOTTOM: patternId=2, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C369/initial_net.png", "targetTopFaceImage": "images/C369/target_top_face.png"}, "__sample_id__": "C369"} +{"taskType": "roll_to_target_top_face", "code": "C370", "name": "Goal Roll C370", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "O", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "K", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "diamond", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "2", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "T", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "O", "rotation": 270}, "FRONT": {"patternId": "K", "rotation": 90}, "RIGHT": {"patternId": "diamond", "rotation": 90}, "BACK": {"patternId": "2", "rotation": 90}, "LEFT": {"patternId": "T", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 6, "stepNumber": 7, "patternId": "K", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C370/initial_net.png", "targetTopFaceImage": "../images/C370/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 7, "targetRotationOffset": 270, "levelId": 370, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-370.json"}, "rollSequence": ["S", "S", "E", "W", "S", "W", "E", "W", "W"], "observedPathFaces": [{"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "E", "W", "S", "W", "E", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 270}, "FRONT": {"patternId": "K", "rotation": 90}, "RIGHT": {"patternId": "diamond", "rotation": 90}, "BACK": {"patternId": "2", "rotation": 90}, "LEFT": {"patternId": "T", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C370\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=K, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=2, rotation=90]\n[LEFT: patternId=T, rotation=180] [TOP: patternId=O, rotation=270] [RIGHT: patternId=diamond, rotation=90]\n [FRONT: patternId=K, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=2, rotation=90\n- LEFT: patternId=T, rotation=180\n- TOP: patternId=O, rotation=270\n- RIGHT: patternId=diamond, rotation=90\n- FRONT: patternId=K, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C370/initial_net.png", "targetTopFaceImage": "images/C370/target_top_face.png"}, "__sample_id__": "C370"} +{"taskType": "roll_to_target_top_face", "code": "C371", "name": "Goal Roll C371", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "arrow_left", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "star", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "T", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "3", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "U", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "arrow_left", "rotation": 270}, "FRONT": {"patternId": "star", "rotation": 90}, "RIGHT": {"patternId": "T", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 0}, "BOTTOM": {"patternId": "U", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "3", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C371/initial_net.png", "targetTopFaceImage": "../images/C371/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 371, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-371.json"}, "rollSequence": ["E", "S", "W", "S", "S", "E", "W", "N"], "observedPathFaces": [{"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "W", "S", "S", "E", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "arrow_left", "rotation": 270}, "FRONT": {"patternId": "star", "rotation": 90}, "RIGHT": {"patternId": "T", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 0}, "BOTTOM": {"patternId": "U", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C371\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=3, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=3, rotation=0] [TOP: patternId=arrow_left, rotation=270] [RIGHT: patternId=T, rotation=270]\n [FRONT: patternId=star, rotation=90]\n [BOTTOM: patternId=U, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=3, rotation=0\n- TOP: patternId=arrow_left, rotation=270\n- RIGHT: patternId=T, rotation=270\n- FRONT: patternId=star, rotation=90\n- BOTTOM: patternId=U, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C371/initial_net.png", "targetTopFaceImage": "images/C371/target_top_face.png"}, "__sample_id__": "C371"} +{"taskType": "roll_to_target_top_face", "code": "C372", "name": "Goal Roll C372", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "arrow_down", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "L", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "heart", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_right", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "triangle", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "R", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "arrow_down", "rotation": 180}, "FRONT": {"patternId": "L", "rotation": 270}, "RIGHT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "arrow_right", "rotation": 90}, "LEFT": {"patternId": "triangle", "rotation": 0}, "BOTTOM": {"patternId": "R", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 8, "stepNumber": 9, "patternId": "arrow_down", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C372/initial_net.png", "targetTopFaceImage": "../images/C372/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 9, "targetRotationOffset": 180, "levelId": 372, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-372.json"}, "rollSequence": ["N", "W", "N", "N", "W", "W", "S", "E", "E"], "observedPathFaces": [{"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "N", "N", "W", "W", "S", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "arrow_down", "rotation": 180}, "FRONT": {"patternId": "L", "rotation": 270}, "RIGHT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "arrow_right", "rotation": 90}, "LEFT": {"patternId": "triangle", "rotation": 0}, "BOTTOM": {"patternId": "R", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C372\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=arrow_down, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_right, rotation=90]\n[LEFT: patternId=triangle, rotation=0] [TOP: patternId=arrow_down, rotation=180] [RIGHT: patternId=heart, rotation=270]\n [FRONT: patternId=L, rotation=270]\n [BOTTOM: patternId=R, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_right, rotation=90\n- LEFT: patternId=triangle, rotation=0\n- TOP: patternId=arrow_down, rotation=180\n- RIGHT: patternId=heart, rotation=270\n- FRONT: patternId=L, rotation=270\n- BOTTOM: patternId=R, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C372/initial_net.png", "targetTopFaceImage": "images/C372/target_top_face.png"}, "__sample_id__": "C372"} +{"taskType": "roll_to_target_top_face", "code": "C373", "name": "Goal Roll C373", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "H", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "circle", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "V", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "L", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "M", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "O", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "H", "rotation": 180}, "FRONT": {"patternId": "circle", "rotation": 0}, "RIGHT": {"patternId": "V", "rotation": 90}, "BACK": {"patternId": "L", "rotation": 0}, "LEFT": {"patternId": "M", "rotation": 90}, "BOTTOM": {"patternId": "O", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "circle", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C373/initial_net.png", "targetTopFaceImage": "../images/C373/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 6, "targetRotationOffset": 270, "levelId": 373, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-373.json"}, "rollSequence": ["S", "W", "E", "E", "S", "E", "S", "E"], "observedPathFaces": [{"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "E", "E", "S", "E", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "H", "rotation": 180}, "FRONT": {"patternId": "circle", "rotation": 0}, "RIGHT": {"patternId": "V", "rotation": 90}, "BACK": {"patternId": "L", "rotation": 0}, "LEFT": {"patternId": "M", "rotation": 90}, "BOTTOM": {"patternId": "O", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C373\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=circle, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=L, rotation=0]\n[LEFT: patternId=M, rotation=90] [TOP: patternId=H, rotation=180] [RIGHT: patternId=V, rotation=90]\n [FRONT: patternId=circle, rotation=0]\n [BOTTOM: patternId=O, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=L, rotation=0\n- LEFT: patternId=M, rotation=90\n- TOP: patternId=H, rotation=180\n- RIGHT: patternId=V, rotation=90\n- FRONT: patternId=circle, rotation=0\n- BOTTOM: patternId=O, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C373/initial_net.png", "targetTopFaceImage": "images/C373/target_top_face.png"}, "__sample_id__": "C373"} +{"taskType": "roll_to_target_top_face", "code": "C374", "name": "Goal Roll C374", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "1", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "V", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "4", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "H", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "P", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "1", "rotation": 0}, "FRONT": {"patternId": "V", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "4", "rotation": 270}, "LEFT": {"patternId": "H", "rotation": 270}, "BOTTOM": {"patternId": "P", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "4", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C374/initial_net.png", "targetTopFaceImage": "../images/C374/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 3, "targetRotationOffset": 90, "levelId": 374, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-374.json"}, "rollSequence": ["N", "W", "W", "S", "N", "N", "E", "E", "N"], "observedPathFaces": [{"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "W", "S", "N", "N", "E", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "1", "rotation": 0}, "FRONT": {"patternId": "V", "rotation": 0}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "4", "rotation": 270}, "LEFT": {"patternId": "H", "rotation": 270}, "BOTTOM": {"patternId": "P", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C374\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=4, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=4, rotation=270]\n[LEFT: patternId=H, rotation=270] [TOP: patternId=1, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=V, rotation=0]\n [BOTTOM: patternId=P, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=4, rotation=270\n- LEFT: patternId=H, rotation=270\n- TOP: patternId=1, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=V, rotation=0\n- BOTTOM: patternId=P, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C374/initial_net.png", "targetTopFaceImage": "images/C374/target_top_face.png"}, "__sample_id__": "C374"} +{"taskType": "roll_to_target_top_face", "code": "C375", "name": "Goal Roll C375", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "5", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "I", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "B", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "5", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "5", "rotation": 90}, "RIGHT": {"patternId": "I", "rotation": 90}, "BACK": {"patternId": "B", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "5", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "5", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C375/initial_net.png", "targetTopFaceImage": "../images/C375/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 375, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-375.json"}, "rollSequence": ["N", "S", "S", "E", "N", "E", "S", "N"], "observedPathFaces": [{"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "S", "S", "E", "N", "E", "S", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "5", "rotation": 90}, "RIGHT": {"patternId": "I", "rotation": 90}, "BACK": {"patternId": "B", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "5", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C375\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=5, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=B, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=I, rotation=90]\n [FRONT: patternId=5, rotation=90]\n [BOTTOM: patternId=5, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=B, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=I, rotation=90\n- FRONT: patternId=5, rotation=90\n- BOTTOM: patternId=5, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C375/initial_net.png", "targetTopFaceImage": "images/C375/target_top_face.png"}, "__sample_id__": "C375"} +{"taskType": "roll_to_target_top_face", "code": "C376", "name": "Goal Roll C376", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "F", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "plus", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "8", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "6", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "F", "rotation": 0}, "FRONT": {"patternId": "plus", "rotation": 90}, "RIGHT": {"patternId": "8", "rotation": 270}, "BACK": {"patternId": "6", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "6", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C376/initial_net.png", "targetTopFaceImage": "../images/C376/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 2, "targetRotationOffset": 90, "levelId": 376, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-376.json"}, "rollSequence": ["E", "S", "E", "N", "W", "E", "W", "S", "S"], "observedPathFaces": [{"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "E", "N", "W", "E", "W", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "F", "rotation": 0}, "FRONT": {"patternId": "plus", "rotation": 90}, "RIGHT": {"patternId": "8", "rotation": 270}, "BACK": {"patternId": "6", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C376\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=6, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=6, rotation=90]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=F, rotation=0] [RIGHT: patternId=8, rotation=270]\n [FRONT: patternId=plus, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=6, rotation=90\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=F, rotation=0\n- RIGHT: patternId=8, rotation=270\n- FRONT: patternId=plus, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C376/initial_net.png", "targetTopFaceImage": "images/C376/target_top_face.png"}, "__sample_id__": "C376"} +{"taskType": "roll_to_target_top_face", "code": "C377", "name": "Goal Roll C377", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "E", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "6", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "B", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "1", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "A", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "E", "rotation": 0}, "FRONT": {"patternId": "6", "rotation": 270}, "RIGHT": {"patternId": "B", "rotation": 270}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "A", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 7, "stepNumber": 8, "patternId": "6", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C377/initial_net.png", "targetTopFaceImage": "../images/C377/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 8, "targetRotationOffset": 180, "levelId": 377, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-377.json"}, "rollSequence": ["S", "S", "E", "N", "N", "N", "S", "N"], "observedPathFaces": [{"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "E", "N", "N", "N", "S", "N"]}, "legacy_answer": {"TOP": {"patternId": "E", "rotation": 0}, "FRONT": {"patternId": "6", "rotation": 270}, "RIGHT": {"patternId": "B", "rotation": 270}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "A", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C377\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=6, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=1, rotation=180]\n[LEFT: patternId=A, rotation=0] [TOP: patternId=E, rotation=0] [RIGHT: patternId=B, rotation=270]\n [FRONT: patternId=6, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=1, rotation=180\n- LEFT: patternId=A, rotation=0\n- TOP: patternId=E, rotation=0\n- RIGHT: patternId=B, rotation=270\n- FRONT: patternId=6, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C377/initial_net.png", "targetTopFaceImage": "images/C377/target_top_face.png"}, "__sample_id__": "C377"} +{"taskType": "roll_to_target_top_face", "code": "C378", "name": "Goal Roll C378", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "5", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "O", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "T", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "Y", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "8", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "5", "rotation": 180}, "RIGHT": {"patternId": "O", "rotation": 0}, "BACK": {"patternId": "T", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 270}, "BOTTOM": {"patternId": "8", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "5", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C378/initial_net.png", "targetTopFaceImage": "../images/C378/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 2, "targetRotationOffset": 90, "levelId": 378, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-378.json"}, "rollSequence": ["E", "N", "N", "N", "W", "N", "E", "E", "S"], "observedPathFaces": [{"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "N", "N", "W", "N", "E", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "5", "rotation": 180}, "RIGHT": {"patternId": "O", "rotation": 0}, "BACK": {"patternId": "T", "rotation": 0}, "LEFT": {"patternId": "Y", "rotation": 270}, "BOTTOM": {"patternId": "8", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C378\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=5, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=T, rotation=0]\n[LEFT: patternId=Y, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=O, rotation=0]\n [FRONT: patternId=5, rotation=180]\n [BOTTOM: patternId=8, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=T, rotation=0\n- LEFT: patternId=Y, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=O, rotation=0\n- FRONT: patternId=5, rotation=180\n- BOTTOM: patternId=8, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C378/initial_net.png", "targetTopFaceImage": "images/C378/target_top_face.png"}, "__sample_id__": "C378"} +{"taskType": "roll_to_target_top_face", "code": "C379", "name": "Goal Roll C379", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "F", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "B", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "S", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "heart", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "M", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "V", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "F", "rotation": 90}, "FRONT": {"patternId": "B", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 0}, "BACK": {"patternId": "heart", "rotation": 0}, "LEFT": {"patternId": "M", "rotation": 180}, "BOTTOM": {"patternId": "V", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "S", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C379/initial_net.png", "targetTopFaceImage": "../images/C379/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 2, "targetRotationOffset": 270, "levelId": 379, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-379.json"}, "rollSequence": ["N", "W", "N", "S", "N", "W", "W", "N", "N"], "observedPathFaces": [{"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "N", "S", "N", "W", "W", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "F", "rotation": 90}, "FRONT": {"patternId": "B", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 0}, "BACK": {"patternId": "heart", "rotation": 0}, "LEFT": {"patternId": "M", "rotation": 180}, "BOTTOM": {"patternId": "V", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C379\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=S, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=heart, rotation=0]\n[LEFT: patternId=M, rotation=180] [TOP: patternId=F, rotation=90] [RIGHT: patternId=S, rotation=0]\n [FRONT: patternId=B, rotation=0]\n [BOTTOM: patternId=V, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=heart, rotation=0\n- LEFT: patternId=M, rotation=180\n- TOP: patternId=F, rotation=90\n- RIGHT: patternId=S, rotation=0\n- FRONT: patternId=B, rotation=0\n- BOTTOM: patternId=V, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C379/initial_net.png", "targetTopFaceImage": "images/C379/target_top_face.png"}, "__sample_id__": "C379"} +{"taskType": "roll_to_target_top_face", "code": "C380", "name": "Goal Roll C380", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "X", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "diamond", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "F", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "6", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "4", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "X", "rotation": 90}, "FRONT": {"patternId": "diamond", "rotation": 0}, "RIGHT": {"patternId": "F", "rotation": 180}, "BACK": {"patternId": "6", "rotation": 270}, "LEFT": {"patternId": "4", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "diamond", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C380/initial_net.png", "targetTopFaceImage": "../images/C380/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 4, "targetRotationOffset": 180, "levelId": 380, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-380.json"}, "rollSequence": ["N", "N", "E", "S", "W", "W", "S", "E"], "observedPathFaces": [{"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "E", "S", "W", "W", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "X", "rotation": 90}, "FRONT": {"patternId": "diamond", "rotation": 0}, "RIGHT": {"patternId": "F", "rotation": 180}, "BACK": {"patternId": "6", "rotation": 270}, "LEFT": {"patternId": "4", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C380\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=diamond, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=6, rotation=270]\n[LEFT: patternId=4, rotation=270] [TOP: patternId=X, rotation=90] [RIGHT: patternId=F, rotation=180]\n [FRONT: patternId=diamond, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=6, rotation=270\n- LEFT: patternId=4, rotation=270\n- TOP: patternId=X, rotation=90\n- RIGHT: patternId=F, rotation=180\n- FRONT: patternId=diamond, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C380/initial_net.png", "targetTopFaceImage": "images/C380/target_top_face.png"}, "__sample_id__": "C380"} +{"taskType": "roll_to_target_top_face", "code": "C381", "name": "Goal Roll C381", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "C", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "E", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "X", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "5", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "B", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "A", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "C", "rotation": 90}, "FRONT": {"patternId": "E", "rotation": 0}, "RIGHT": {"patternId": "X", "rotation": 0}, "BACK": {"patternId": "5", "rotation": 180}, "LEFT": {"patternId": "B", "rotation": 180}, "BOTTOM": {"patternId": "A", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "5", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C381/initial_net.png", "targetTopFaceImage": "../images/C381/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 3, "targetRotationOffset": 90, "levelId": 381, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-381.json"}, "rollSequence": ["N", "N", "N", "W", "N", "E", "W", "N"], "observedPathFaces": [{"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "N", "W", "N", "E", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "C", "rotation": 90}, "FRONT": {"patternId": "E", "rotation": 0}, "RIGHT": {"patternId": "X", "rotation": 0}, "BACK": {"patternId": "5", "rotation": 180}, "LEFT": {"patternId": "B", "rotation": 180}, "BOTTOM": {"patternId": "A", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C381\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=5, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=5, rotation=180]\n[LEFT: patternId=B, rotation=180] [TOP: patternId=C, rotation=90] [RIGHT: patternId=X, rotation=0]\n [FRONT: patternId=E, rotation=0]\n [BOTTOM: patternId=A, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=5, rotation=180\n- LEFT: patternId=B, rotation=180\n- TOP: patternId=C, rotation=90\n- RIGHT: patternId=X, rotation=0\n- FRONT: patternId=E, rotation=0\n- BOTTOM: patternId=A, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C381/initial_net.png", "targetTopFaceImage": "images/C381/target_top_face.png"}, "__sample_id__": "C381"} +{"taskType": "roll_to_target_top_face", "code": "C382", "name": "Goal Roll C382", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "Y", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "X", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "8", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "heart", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "T", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "Y", "rotation": 180}, "FRONT": {"patternId": "X", "rotation": 270}, "RIGHT": {"patternId": "8", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "heart", "rotation": 90}, "BOTTOM": {"patternId": "T", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "8", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C382/initial_net.png", "targetTopFaceImage": "../images/C382/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 382, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-382.json"}, "rollSequence": ["W", "S", "E", "S", "W", "S", "E", "E"], "observedPathFaces": [{"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "E", "S", "W", "S", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "Y", "rotation": 180}, "FRONT": {"patternId": "X", "rotation": 270}, "RIGHT": {"patternId": "8", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "heart", "rotation": 90}, "BOTTOM": {"patternId": "T", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C382\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=8, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=heart, rotation=90] [TOP: patternId=Y, rotation=180] [RIGHT: patternId=8, rotation=0]\n [FRONT: patternId=X, rotation=270]\n [BOTTOM: patternId=T, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=heart, rotation=90\n- TOP: patternId=Y, rotation=180\n- RIGHT: patternId=8, rotation=0\n- FRONT: patternId=X, rotation=270\n- BOTTOM: patternId=T, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C382/initial_net.png", "targetTopFaceImage": "images/C382/target_top_face.png"}, "__sample_id__": "C382"} +{"taskType": "roll_to_target_top_face", "code": "C383", "name": "Goal Roll C383", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "star", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "J", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "R", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "Z", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "N", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "V", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "star", "rotation": 0}, "FRONT": {"patternId": "J", "rotation": 180}, "RIGHT": {"patternId": "R", "rotation": 0}, "BACK": {"patternId": "Z", "rotation": 270}, "LEFT": {"patternId": "N", "rotation": 270}, "BOTTOM": {"patternId": "V", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "Z", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C383/initial_net.png", "targetTopFaceImage": "../images/C383/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 4, "targetRotationOffset": 90, "levelId": 383, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-383.json"}, "rollSequence": ["S", "E", "S", "W", "N", "W", "N", "S", "W"], "observedPathFaces": [{"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "S", "W", "N", "W", "N", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "star", "rotation": 0}, "FRONT": {"patternId": "J", "rotation": 180}, "RIGHT": {"patternId": "R", "rotation": 0}, "BACK": {"patternId": "Z", "rotation": 270}, "LEFT": {"patternId": "N", "rotation": 270}, "BOTTOM": {"patternId": "V", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C383\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=Z, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=Z, rotation=270]\n[LEFT: patternId=N, rotation=270] [TOP: patternId=star, rotation=0] [RIGHT: patternId=R, rotation=0]\n [FRONT: patternId=J, rotation=180]\n [BOTTOM: patternId=V, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Z, rotation=270\n- LEFT: patternId=N, rotation=270\n- TOP: patternId=star, rotation=0\n- RIGHT: patternId=R, rotation=0\n- FRONT: patternId=J, rotation=180\n- BOTTOM: patternId=V, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C383/initial_net.png", "targetTopFaceImage": "images/C383/target_top_face.png"}, "__sample_id__": "C383"} +{"taskType": "roll_to_target_top_face", "code": "C384", "name": "Goal Roll C384", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "Y", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "K", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "P", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "J", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "R", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_left", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "Y", "rotation": 0}, "FRONT": {"patternId": "K", "rotation": 180}, "RIGHT": {"patternId": "P", "rotation": 270}, "BACK": {"patternId": "J", "rotation": 180}, "LEFT": {"patternId": "R", "rotation": 180}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "P", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C384/initial_net.png", "targetTopFaceImage": "../images/C384/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 6, "targetRotationOffset": 90, "levelId": 384, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-384.json"}, "rollSequence": ["E", "E", "E", "N", "W", "S", "W", "S", "E"], "observedPathFaces": [{"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "E", "N", "W", "S", "W", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "Y", "rotation": 0}, "FRONT": {"patternId": "K", "rotation": 180}, "RIGHT": {"patternId": "P", "rotation": 270}, "BACK": {"patternId": "J", "rotation": 180}, "LEFT": {"patternId": "R", "rotation": 180}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C384\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=P, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=J, rotation=180]\n[LEFT: patternId=R, rotation=180] [TOP: patternId=Y, rotation=0] [RIGHT: patternId=P, rotation=270]\n [FRONT: patternId=K, rotation=180]\n [BOTTOM: patternId=arrow_left, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=J, rotation=180\n- LEFT: patternId=R, rotation=180\n- TOP: patternId=Y, rotation=0\n- RIGHT: patternId=P, rotation=270\n- FRONT: patternId=K, rotation=180\n- BOTTOM: patternId=arrow_left, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C384/initial_net.png", "targetTopFaceImage": "images/C384/target_top_face.png"}, "__sample_id__": "C384"} +{"taskType": "roll_to_target_top_face", "code": "C385", "name": "Goal Roll C385", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "W", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "square", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "R", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "1", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "7", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "K", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "W", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 270}, "RIGHT": {"patternId": "R", "rotation": 90}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "7", "rotation": 90}, "BOTTOM": {"patternId": "K", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 7, "stepNumber": 8, "patternId": "K", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C385/initial_net.png", "targetTopFaceImage": "../images/C385/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 8, "targetRotationOffset": 180, "levelId": 385, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-385.json"}, "rollSequence": ["W", "S", "W", "N", "N", "W", "N", "W"], "observedPathFaces": [{"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "W", "N", "N", "W", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "W", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 270}, "RIGHT": {"patternId": "R", "rotation": 90}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "7", "rotation": 90}, "BOTTOM": {"patternId": "K", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C385\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=K, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=1, rotation=180]\n[LEFT: patternId=7, rotation=90] [TOP: patternId=W, rotation=0] [RIGHT: patternId=R, rotation=90]\n [FRONT: patternId=square, rotation=270]\n [BOTTOM: patternId=K, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=1, rotation=180\n- LEFT: patternId=7, rotation=90\n- TOP: patternId=W, rotation=0\n- RIGHT: patternId=R, rotation=90\n- FRONT: patternId=square, rotation=270\n- BOTTOM: patternId=K, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C385/initial_net.png", "targetTopFaceImage": "images/C385/target_top_face.png"}, "__sample_id__": "C385"} +{"taskType": "roll_to_target_top_face", "code": "C386", "name": "Goal Roll C386", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "E", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "1", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "J", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "U", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "7", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "E", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 0}, "BACK": {"patternId": "J", "rotation": 270}, "LEFT": {"patternId": "U", "rotation": 90}, "BOTTOM": {"patternId": "7", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "E", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C386/initial_net.png", "targetTopFaceImage": "../images/C386/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 3, "targetRotationOffset": 90, "levelId": 386, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-386.json"}, "rollSequence": ["E", "N", "W", "N", "N", "N", "S", "E"], "observedPathFaces": [{"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "W", "N", "N", "N", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "E", "rotation": 180}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 0}, "BACK": {"patternId": "J", "rotation": 270}, "LEFT": {"patternId": "U", "rotation": 90}, "BOTTOM": {"patternId": "7", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C386\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=E, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=J, rotation=270]\n[LEFT: patternId=U, rotation=90] [TOP: patternId=E, rotation=180] [RIGHT: patternId=1, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=7, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=J, rotation=270\n- LEFT: patternId=U, rotation=90\n- TOP: patternId=E, rotation=180\n- RIGHT: patternId=1, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=7, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C386/initial_net.png", "targetTopFaceImage": "images/C386/target_top_face.png"}, "__sample_id__": "C386"} +{"taskType": "roll_to_target_top_face", "code": "C387", "name": "Goal Roll C387", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "I", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "A", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Z", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "7", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "M", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "F", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "I", "rotation": 180}, "FRONT": {"patternId": "A", "rotation": 90}, "RIGHT": {"patternId": "Z", "rotation": 180}, "BACK": {"patternId": "7", "rotation": 90}, "LEFT": {"patternId": "M", "rotation": 0}, "BOTTOM": {"patternId": "F", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 8, "stepNumber": 9, "patternId": "F", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C387/initial_net.png", "targetTopFaceImage": "../images/C387/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 9, "targetRotationOffset": 90, "levelId": 387, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-387.json"}, "rollSequence": ["N", "E", "W", "N", "N", "W", "N", "E", "E"], "observedPathFaces": [{"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "W", "N", "N", "W", "N", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "I", "rotation": 180}, "FRONT": {"patternId": "A", "rotation": 90}, "RIGHT": {"patternId": "Z", "rotation": 180}, "BACK": {"patternId": "7", "rotation": 90}, "LEFT": {"patternId": "M", "rotation": 0}, "BOTTOM": {"patternId": "F", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C387\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=F, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=7, rotation=90]\n[LEFT: patternId=M, rotation=0] [TOP: patternId=I, rotation=180] [RIGHT: patternId=Z, rotation=180]\n [FRONT: patternId=A, rotation=90]\n [BOTTOM: patternId=F, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=7, rotation=90\n- LEFT: patternId=M, rotation=0\n- TOP: patternId=I, rotation=180\n- RIGHT: patternId=Z, rotation=180\n- FRONT: patternId=A, rotation=90\n- BOTTOM: patternId=F, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C387/initial_net.png", "targetTopFaceImage": "images/C387/target_top_face.png"}, "__sample_id__": "C387"} +{"taskType": "roll_to_target_top_face", "code": "C388", "name": "Goal Roll C388", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_right", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "V", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "H", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "square", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 0}, "BACK": {"patternId": "V", "rotation": 0}, "LEFT": {"patternId": "H", "rotation": 0}, "BOTTOM": {"patternId": "square", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "arrow_right", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C388/initial_net.png", "targetTopFaceImage": "../images/C388/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 388, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-388.json"}, "rollSequence": ["W", "N", "E", "N", "W", "W", "S", "S"], "observedPathFaces": [{"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "E", "N", "W", "W", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 0}, "BACK": {"patternId": "V", "rotation": 0}, "LEFT": {"patternId": "H", "rotation": 0}, "BOTTOM": {"patternId": "square", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C388\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=arrow_right, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=V, rotation=0]\n[LEFT: patternId=H, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=arrow_right, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=square, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=V, rotation=0\n- LEFT: patternId=H, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=arrow_right, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=square, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C388/initial_net.png", "targetTopFaceImage": "images/C388/target_top_face.png"}, "__sample_id__": "C388"} +{"taskType": "roll_to_target_top_face", "code": "C389", "name": "Goal Roll C389", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "G", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "arrow_right", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "I", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "I", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_left", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "G", "rotation": 180}, "FRONT": {"patternId": "arrow_right", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 270}, "BACK": {"patternId": "I", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_left", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "G", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C389/initial_net.png", "targetTopFaceImage": "../images/C389/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 4, "targetRotationOffset": 90, "levelId": 389, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-389.json"}, "rollSequence": ["S", "S", "N", "N", "E", "N", "W", "W"], "observedPathFaces": [{"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "N", "N", "E", "N", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "G", "rotation": 180}, "FRONT": {"patternId": "arrow_right", "rotation": 0}, "RIGHT": {"patternId": "I", "rotation": 270}, "BACK": {"patternId": "I", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_left", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C389\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=G, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=I, rotation=270]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=G, rotation=180] [RIGHT: patternId=I, rotation=270]\n [FRONT: patternId=arrow_right, rotation=0]\n [BOTTOM: patternId=arrow_left, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=I, rotation=270\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=G, rotation=180\n- RIGHT: patternId=I, rotation=270\n- FRONT: patternId=arrow_right, rotation=0\n- BOTTOM: patternId=arrow_left, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C389/initial_net.png", "targetTopFaceImage": "images/C389/target_top_face.png"}, "__sample_id__": "C389"} +{"taskType": "roll_to_target_top_face", "code": "C390", "name": "Goal Roll C390", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "circle", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "7", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "T", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "C", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "7", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "circle", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "T", "rotation": 0}, "LEFT": {"patternId": "C", "rotation": 90}, "BOTTOM": {"patternId": "7", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "T", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C390/initial_net.png", "targetTopFaceImage": "../images/C390/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 6, "targetRotationOffset": 270, "levelId": 390, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-390.json"}, "rollSequence": ["N", "W", "S", "W", "E", "W", "W", "N"], "observedPathFaces": [{"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "S", "W", "E", "W", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "circle", "rotation": 0}, "FRONT": {"patternId": "7", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "T", "rotation": 0}, "LEFT": {"patternId": "C", "rotation": 90}, "BOTTOM": {"patternId": "7", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C390\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=T, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=T, rotation=0]\n[LEFT: patternId=C, rotation=90] [TOP: patternId=circle, rotation=0] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=7, rotation=90]\n [BOTTOM: patternId=7, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=T, rotation=0\n- LEFT: patternId=C, rotation=90\n- TOP: patternId=circle, rotation=0\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=7, rotation=90\n- BOTTOM: patternId=7, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C390/initial_net.png", "targetTopFaceImage": "images/C390/target_top_face.png"}, "__sample_id__": "C390"} +{"taskType": "roll_to_target_top_face", "code": "C391", "name": "Goal Roll C391", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "X", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "7", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "triangle", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "G", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "heart", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "B", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "X", "rotation": 90}, "FRONT": {"patternId": "7", "rotation": 180}, "RIGHT": {"patternId": "triangle", "rotation": 180}, "BACK": {"patternId": "G", "rotation": 90}, "LEFT": {"patternId": "heart", "rotation": 90}, "BOTTOM": {"patternId": "B", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "G", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C391/initial_net.png", "targetTopFaceImage": "../images/C391/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 391, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-391.json"}, "rollSequence": ["S", "E", "S", "W", "S", "W", "S", "W", "N"], "observedPathFaces": [{"patternId": "7", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "S", "W", "S", "W", "S", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "X", "rotation": 90}, "FRONT": {"patternId": "7", "rotation": 180}, "RIGHT": {"patternId": "triangle", "rotation": 180}, "BACK": {"patternId": "G", "rotation": 90}, "LEFT": {"patternId": "heart", "rotation": 90}, "BOTTOM": {"patternId": "B", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C391\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=G, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=G, rotation=90]\n[LEFT: patternId=heart, rotation=90] [TOP: patternId=X, rotation=90] [RIGHT: patternId=triangle, rotation=180]\n [FRONT: patternId=7, rotation=180]\n [BOTTOM: patternId=B, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=G, rotation=90\n- LEFT: patternId=heart, rotation=90\n- TOP: patternId=X, rotation=90\n- RIGHT: patternId=triangle, rotation=180\n- FRONT: patternId=7, rotation=180\n- BOTTOM: patternId=B, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C391/initial_net.png", "targetTopFaceImage": "images/C391/target_top_face.png"}, "__sample_id__": "C391"} +{"taskType": "roll_to_target_top_face", "code": "C392", "name": "Goal Roll C392", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "diamond", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Y", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_down", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "V", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "O", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "diamond", "rotation": 180}, "RIGHT": {"patternId": "Y", "rotation": 180}, "BACK": {"patternId": "arrow_down", "rotation": 270}, "LEFT": {"patternId": "V", "rotation": 180}, "BOTTOM": {"patternId": "O", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 6, "stepNumber": 7, "patternId": "Y", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C392/initial_net.png", "targetTopFaceImage": "../images/C392/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 7, "targetRotationOffset": 90, "levelId": 392, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-392.json"}, "rollSequence": ["W", "E", "E", "N", "W", "W", "N", "S"], "observedPathFaces": [{"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "E", "E", "N", "W", "W", "N", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "diamond", "rotation": 180}, "RIGHT": {"patternId": "Y", "rotation": 180}, "BACK": {"patternId": "arrow_down", "rotation": 270}, "LEFT": {"patternId": "V", "rotation": 180}, "BOTTOM": {"patternId": "O", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C392\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=Y, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_down, rotation=270]\n[LEFT: patternId=V, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=Y, rotation=180]\n [FRONT: patternId=diamond, rotation=180]\n [BOTTOM: patternId=O, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_down, rotation=270\n- LEFT: patternId=V, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=Y, rotation=180\n- FRONT: patternId=diamond, rotation=180\n- BOTTOM: patternId=O, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C392/initial_net.png", "targetTopFaceImage": "images/C392/target_top_face.png"}, "__sample_id__": "C392"} +{"taskType": "roll_to_target_top_face", "code": "C393", "name": "Goal Roll C393", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "triangle", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "D", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "S", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "C", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "4", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "triangle", "rotation": 90}, "RIGHT": {"patternId": "D", "rotation": 0}, "BACK": {"patternId": "S", "rotation": 0}, "LEFT": {"patternId": "C", "rotation": 0}, "BOTTOM": {"patternId": "4", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "S", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C393/initial_net.png", "targetTopFaceImage": "../images/C393/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 2, "targetRotationOffset": 270, "levelId": 393, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-393.json"}, "rollSequence": ["W", "S", "S", "S", "E", "S", "N", "W"], "observedPathFaces": [{"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "S", "S", "E", "S", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "triangle", "rotation": 90}, "RIGHT": {"patternId": "D", "rotation": 0}, "BACK": {"patternId": "S", "rotation": 0}, "LEFT": {"patternId": "C", "rotation": 0}, "BOTTOM": {"patternId": "4", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C393\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=S, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=S, rotation=0]\n[LEFT: patternId=C, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=D, rotation=0]\n [FRONT: patternId=triangle, rotation=90]\n [BOTTOM: patternId=4, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=S, rotation=0\n- LEFT: patternId=C, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=D, rotation=0\n- FRONT: patternId=triangle, rotation=90\n- BOTTOM: patternId=4, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C393/initial_net.png", "targetTopFaceImage": "images/C393/target_top_face.png"}, "__sample_id__": "C393"} +{"taskType": "roll_to_target_top_face", "code": "C394", "name": "Goal Roll C394", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "X", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "J", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "2", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "W", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_up", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "X", "rotation": 180}, "RIGHT": {"patternId": "J", "rotation": 0}, "BACK": {"patternId": "2", "rotation": 0}, "LEFT": {"patternId": "W", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "2", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C394/initial_net.png", "targetTopFaceImage": "../images/C394/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 394, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-394.json"}, "rollSequence": ["S", "W", "W", "N", "W", "E", "E", "W"], "observedPathFaces": [{"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "W", "N", "W", "E", "E", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "X", "rotation": 180}, "RIGHT": {"patternId": "J", "rotation": 0}, "BACK": {"patternId": "2", "rotation": 0}, "LEFT": {"patternId": "W", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C394\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=2, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=2, rotation=0]\n[LEFT: patternId=W, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=J, rotation=0]\n [FRONT: patternId=X, rotation=180]\n [BOTTOM: patternId=arrow_up, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=2, rotation=0\n- LEFT: patternId=W, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=J, rotation=0\n- FRONT: patternId=X, rotation=180\n- BOTTOM: patternId=arrow_up, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C394/initial_net.png", "targetTopFaceImage": "images/C394/target_top_face.png"}, "__sample_id__": "C394"} +{"taskType": "roll_to_target_top_face", "code": "C395", "name": "Goal Roll C395", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "U", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "K", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "triangle", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "plus", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "K", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "O", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "U", "rotation": 90}, "FRONT": {"patternId": "K", "rotation": 0}, "RIGHT": {"patternId": "triangle", "rotation": 180}, "BACK": {"patternId": "plus", "rotation": 90}, "LEFT": {"patternId": "K", "rotation": 270}, "BOTTOM": {"patternId": "O", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "O", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C395/initial_net.png", "targetTopFaceImage": "../images/C395/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 3, "targetRotationOffset": 90, "levelId": 395, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-395.json"}, "rollSequence": ["S", "E", "S", "S", "W", "W", "W", "S", "S"], "observedPathFaces": [{"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "S", "S", "W", "W", "W", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "U", "rotation": 90}, "FRONT": {"patternId": "K", "rotation": 0}, "RIGHT": {"patternId": "triangle", "rotation": 180}, "BACK": {"patternId": "plus", "rotation": 90}, "LEFT": {"patternId": "K", "rotation": 270}, "BOTTOM": {"patternId": "O", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C395\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=O, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=plus, rotation=90]\n[LEFT: patternId=K, rotation=270] [TOP: patternId=U, rotation=90] [RIGHT: patternId=triangle, rotation=180]\n [FRONT: patternId=K, rotation=0]\n [BOTTOM: patternId=O, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=plus, rotation=90\n- LEFT: patternId=K, rotation=270\n- TOP: patternId=U, rotation=90\n- RIGHT: patternId=triangle, rotation=180\n- FRONT: patternId=K, rotation=0\n- BOTTOM: patternId=O, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C395/initial_net.png", "targetTopFaceImage": "images/C395/target_top_face.png"}, "__sample_id__": "C395"} +{"taskType": "roll_to_target_top_face", "code": "C396", "name": "Goal Roll C396", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "2", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "C", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "K", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "Z", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "smile", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "F", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "2", "rotation": 180}, "FRONT": {"patternId": "C", "rotation": 180}, "RIGHT": {"patternId": "K", "rotation": 0}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "smile", "rotation": 90}, "BOTTOM": {"patternId": "F", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 8, "stepNumber": 9, "patternId": "F", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C396/initial_net.png", "targetTopFaceImage": "../images/C396/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 9, "targetRotationOffset": 90, "levelId": 396, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-396.json"}, "rollSequence": ["N", "E", "E", "S", "W", "W", "S", "W", "N"], "observedPathFaces": [{"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "E", "S", "W", "W", "S", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "2", "rotation": 180}, "FRONT": {"patternId": "C", "rotation": 180}, "RIGHT": {"patternId": "K", "rotation": 0}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "smile", "rotation": 90}, "BOTTOM": {"patternId": "F", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C396\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=F, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=Z, rotation=90]\n[LEFT: patternId=smile, rotation=90] [TOP: patternId=2, rotation=180] [RIGHT: patternId=K, rotation=0]\n [FRONT: patternId=C, rotation=180]\n [BOTTOM: patternId=F, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Z, rotation=90\n- LEFT: patternId=smile, rotation=90\n- TOP: patternId=2, rotation=180\n- RIGHT: patternId=K, rotation=0\n- FRONT: patternId=C, rotation=180\n- BOTTOM: patternId=F, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C396/initial_net.png", "targetTopFaceImage": "images/C396/target_top_face.png"}, "__sample_id__": "C396"} +{"taskType": "roll_to_target_top_face", "code": "C397", "name": "Goal Roll C397", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "D", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "P", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_up", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "C", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "K", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "D", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "P", "rotation": 270}, "BACK": {"patternId": "arrow_up", "rotation": 270}, "LEFT": {"patternId": "C", "rotation": 90}, "BOTTOM": {"patternId": "K", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 7, "stepNumber": 8, "patternId": "P", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C397/initial_net.png", "targetTopFaceImage": "../images/C397/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 8, "targetRotationOffset": 90, "levelId": 397, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-397.json"}, "rollSequence": ["E", "E", "N", "N", "S", "W", "N", "N"], "observedPathFaces": [{"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "N", "N", "S", "W", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "D", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "P", "rotation": 270}, "BACK": {"patternId": "arrow_up", "rotation": 270}, "LEFT": {"patternId": "C", "rotation": 90}, "BOTTOM": {"patternId": "K", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C397\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=P, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_up, rotation=270]\n[LEFT: patternId=C, rotation=90] [TOP: patternId=D, rotation=270] [RIGHT: patternId=P, rotation=270]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=K, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_up, rotation=270\n- LEFT: patternId=C, rotation=90\n- TOP: patternId=D, rotation=270\n- RIGHT: patternId=P, rotation=270\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=K, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C397/initial_net.png", "targetTopFaceImage": "images/C397/target_top_face.png"}, "__sample_id__": "C397"} +{"taskType": "roll_to_target_top_face", "code": "C398", "name": "Goal Roll C398", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "I", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "1", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "1", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "Y", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_left", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "I", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 270}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "Y", "rotation": 270}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 6, "stepNumber": 7, "patternId": "1", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C398/initial_net.png", "targetTopFaceImage": "../images/C398/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 7, "targetRotationOffset": 180, "levelId": 398, "moveCount": 8, "sourceLevelPath": "levels/reconstruct/generated-398.json"}, "rollSequence": ["E", "E", "N", "E", "N", "W", "S", "W"], "observedPathFaces": [{"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "N", "E", "N", "W", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "I", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 270}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "Y", "rotation": 270}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C398\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=1, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=1, rotation=180]\n[LEFT: patternId=Y, rotation=270] [TOP: patternId=I, rotation=270] [RIGHT: patternId=1, rotation=270]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=arrow_left, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=1, rotation=180\n- LEFT: patternId=Y, rotation=270\n- TOP: patternId=I, rotation=270\n- RIGHT: patternId=1, rotation=270\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=arrow_left, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C398/initial_net.png", "targetTopFaceImage": "images/C398/target_top_face.png"}, "__sample_id__": "C398"} +{"taskType": "roll_to_target_top_face", "code": "C399", "name": "Goal Roll C399", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "square", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "arrow_down", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "R", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "C", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_down", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "square", "rotation": 90}, "FRONT": {"patternId": "arrow_down", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "R", "rotation": 90}, "LEFT": {"patternId": "C", "rotation": 180}, "BOTTOM": {"patternId": "arrow_down", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "square", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C399/initial_net.png", "targetTopFaceImage": "../images/C399/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 4, "targetRotationOffset": 270, "levelId": 399, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-399.json"}, "rollSequence": ["N", "W", "W", "S", "N", "N", "E", "N", "S"], "observedPathFaces": [{"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "W", "S", "N", "N", "E", "N", "S"]}, "legacy_answer": {"TOP": {"patternId": "square", "rotation": 90}, "FRONT": {"patternId": "arrow_down", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "R", "rotation": 90}, "LEFT": {"patternId": "C", "rotation": 180}, "BOTTOM": {"patternId": "arrow_down", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C399\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=square, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=R, rotation=90]\n[LEFT: patternId=C, rotation=180] [TOP: patternId=square, rotation=90] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=arrow_down, rotation=270]\n [BOTTOM: patternId=arrow_down, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=R, rotation=90\n- LEFT: patternId=C, rotation=180\n- TOP: patternId=square, rotation=90\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=arrow_down, rotation=270\n- BOTTOM: patternId=arrow_down, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C399/initial_net.png", "targetTopFaceImage": "images/C399/target_top_face.png"}, "__sample_id__": "C399"} +{"taskType": "roll_to_target_top_face", "code": "C400", "name": "Goal Roll C400", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "N", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "circle", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Q", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "V", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "G", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "N", "rotation": 180}, "FRONT": {"patternId": "circle", "rotation": 270}, "RIGHT": {"patternId": "Q", "rotation": 0}, "BACK": {"patternId": "V", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "G", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 8, "stepNumber": 9, "patternId": "V", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C400/initial_net.png", "targetTopFaceImage": "../images/C400/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 9, "targetRotationOffset": 180, "levelId": 400, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-400.json"}, "rollSequence": ["S", "E", "E", "W", "W", "S", "N", "N", "S"], "observedPathFaces": [{"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "E", "W", "W", "S", "N", "N", "S"]}, "legacy_answer": {"TOP": {"patternId": "N", "rotation": 180}, "FRONT": {"patternId": "circle", "rotation": 270}, "RIGHT": {"patternId": "Q", "rotation": 0}, "BACK": {"patternId": "V", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "G", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C400\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=V, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=V, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=N, rotation=180] [RIGHT: patternId=Q, rotation=0]\n [FRONT: patternId=circle, rotation=270]\n [BOTTOM: patternId=G, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=V, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=N, rotation=180\n- RIGHT: patternId=Q, rotation=0\n- FRONT: patternId=circle, rotation=270\n- BOTTOM: patternId=G, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C400/initial_net.png", "targetTopFaceImage": "images/C400/target_top_face.png"}, "__sample_id__": "C400"} +{"taskType": "roll_to_target_top_face", "code": "C401", "name": "Goal Roll C401", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "star", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "2", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "L", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "F", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "O", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "R", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "star", "rotation": 180}, "FRONT": {"patternId": "2", "rotation": 90}, "RIGHT": {"patternId": "L", "rotation": 180}, "BACK": {"patternId": "F", "rotation": 180}, "LEFT": {"patternId": "O", "rotation": 90}, "BOTTOM": {"patternId": "R", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "O", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C401/initial_net.png", "targetTopFaceImage": "../images/C401/target_top_face.png"}, "metadata": {"difficulty": 4, "tier": 4, "targetStepNumber": 6, "targetRotationOffset": 90, "levelId": 401, "moveCount": 9, "sourceLevelPath": "levels/reconstruct/generated-401.json"}, "rollSequence": ["W", "E", "S", "W", "W", "W", "S", "S", "W"], "observedPathFaces": [{"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "E", "S", "W", "W", "W", "S", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "star", "rotation": 180}, "FRONT": {"patternId": "2", "rotation": 90}, "RIGHT": {"patternId": "L", "rotation": 180}, "BACK": {"patternId": "F", "rotation": 180}, "LEFT": {"patternId": "O", "rotation": 90}, "BOTTOM": {"patternId": "R", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C401\n- task_type: roll_to_target_top_face\n- difficulty: 4\n- target_top_face: patternId=O, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=F, rotation=180]\n[LEFT: patternId=O, rotation=90] [TOP: patternId=star, rotation=180] [RIGHT: patternId=L, rotation=180]\n [FRONT: patternId=2, rotation=90]\n [BOTTOM: patternId=R, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=F, rotation=180\n- LEFT: patternId=O, rotation=90\n- TOP: patternId=star, rotation=180\n- RIGHT: patternId=L, rotation=180\n- FRONT: patternId=2, rotation=90\n- BOTTOM: patternId=R, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C401/initial_net.png", "targetTopFaceImage": "images/C401/target_top_face.png"}, "__sample_id__": "C401"} +{"taskType": "roll_to_target_top_face", "code": "C402", "name": "Goal Roll C402", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "M", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "circle", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "D", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "7", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "smile", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "M", "rotation": 180}, "FRONT": {"patternId": "circle", "rotation": 90}, "RIGHT": {"patternId": "D", "rotation": 270}, "BACK": {"patternId": "7", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "smile", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "smile", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C402/initial_net.png", "targetTopFaceImage": "../images/C402/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 2, "targetRotationOffset": 270, "levelId": 402, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-402.json"}, "rollSequence": ["S", "S", "N", "E", "N", "E", "W", "S", "W", "S"], "observedPathFaces": [{"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "N", "E", "N", "E", "W", "S", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "M", "rotation": 180}, "FRONT": {"patternId": "circle", "rotation": 90}, "RIGHT": {"patternId": "D", "rotation": 270}, "BACK": {"patternId": "7", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "smile", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C402\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=smile, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=7, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=M, rotation=180] [RIGHT: patternId=D, rotation=270]\n [FRONT: patternId=circle, rotation=90]\n [BOTTOM: patternId=smile, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=7, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=M, rotation=180\n- RIGHT: patternId=D, rotation=270\n- FRONT: patternId=circle, rotation=90\n- BOTTOM: patternId=smile, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C402/initial_net.png", "targetTopFaceImage": "images/C402/target_top_face.png"}, "__sample_id__": "C402"} +{"taskType": "roll_to_target_top_face", "code": "C403", "name": "Goal Roll C403", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "diamond", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "N", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "triangle", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "plus", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "diamond", "rotation": 270}, "FRONT": {"patternId": "N", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "triangle", "rotation": 90}, "LEFT": {"patternId": "plus", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "triangle", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C403/initial_net.png", "targetTopFaceImage": "../images/C403/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 6, "targetRotationOffset": 90, "levelId": 403, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-403.json"}, "rollSequence": ["W", "W", "E", "N", "S", "S", "W", "W", "N", "E"], "observedPathFaces": [{"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "E", "N", "S", "S", "W", "W", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "diamond", "rotation": 270}, "FRONT": {"patternId": "N", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "triangle", "rotation": 90}, "LEFT": {"patternId": "plus", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C403\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=triangle, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=triangle, rotation=90]\n[LEFT: patternId=plus, rotation=0] [TOP: patternId=diamond, rotation=270] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=N, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=triangle, rotation=90\n- LEFT: patternId=plus, rotation=0\n- TOP: patternId=diamond, rotation=270\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=N, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C403/initial_net.png", "targetTopFaceImage": "images/C403/target_top_face.png"}, "__sample_id__": "C403"} +{"taskType": "roll_to_target_top_face", "code": "C404", "name": "Goal Roll C404", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "O", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "6", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "9", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "3", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "O", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 90}, "BACK": {"patternId": "9", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "3", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C404/initial_net.png", "targetTopFaceImage": "../images/C404/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 4, "targetRotationOffset": 270, "levelId": 404, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-404.json"}, "rollSequence": ["W", "W", "N", "W", "S", "E", "W", "S", "E", "E"], "observedPathFaces": [{"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "N", "W", "S", "E", "W", "S", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "6", "rotation": 90}, "BACK": {"patternId": "9", "rotation": 0}, "LEFT": {"patternId": "3", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C404\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=3, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=9, rotation=0]\n[LEFT: patternId=3, rotation=90] [TOP: patternId=O, rotation=90] [RIGHT: patternId=6, rotation=90]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=9, rotation=0\n- LEFT: patternId=3, rotation=90\n- TOP: patternId=O, rotation=90\n- RIGHT: patternId=6, rotation=90\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C404/initial_net.png", "targetTopFaceImage": "images/C404/target_top_face.png"}, "__sample_id__": "C404"} +{"taskType": "roll_to_target_top_face", "code": "C405", "name": "Goal Roll C405", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "N", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "9", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "D", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "plus", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "L", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "N", "rotation": 180}, "FRONT": {"patternId": "9", "rotation": 0}, "RIGHT": {"patternId": "D", "rotation": 0}, "BACK": {"patternId": "plus", "rotation": 90}, "LEFT": {"patternId": "L", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 7, "stepNumber": 8, "patternId": "9", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C405/initial_net.png", "targetTopFaceImage": "../images/C405/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 8, "targetRotationOffset": 180, "levelId": 405, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-405.json"}, "rollSequence": ["E", "S", "E", "N", "E", "S", "E", "N", "W", "E"], "observedPathFaces": [{"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "E", "N", "E", "S", "E", "N", "W", "E"]}, "legacy_answer": {"TOP": {"patternId": "N", "rotation": 180}, "FRONT": {"patternId": "9", "rotation": 0}, "RIGHT": {"patternId": "D", "rotation": 0}, "BACK": {"patternId": "plus", "rotation": 90}, "LEFT": {"patternId": "L", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C405\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=9, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=plus, rotation=90]\n[LEFT: patternId=L, rotation=180] [TOP: patternId=N, rotation=180] [RIGHT: patternId=D, rotation=0]\n [FRONT: patternId=9, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=plus, rotation=90\n- LEFT: patternId=L, rotation=180\n- TOP: patternId=N, rotation=180\n- RIGHT: patternId=D, rotation=0\n- FRONT: patternId=9, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C405/initial_net.png", "targetTopFaceImage": "images/C405/target_top_face.png"}, "__sample_id__": "C405"} +{"taskType": "roll_to_target_top_face", "code": "C406", "name": "Goal Roll C406", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "P", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "Y", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "X", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "L", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "Y", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "C", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "P", "rotation": 180}, "FRONT": {"patternId": "Y", "rotation": 0}, "RIGHT": {"patternId": "X", "rotation": 0}, "BACK": {"patternId": "L", "rotation": 180}, "LEFT": {"patternId": "Y", "rotation": 270}, "BOTTOM": {"patternId": "C", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 6, "stepNumber": 7, "patternId": "Y", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C406/initial_net.png", "targetTopFaceImage": "../images/C406/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 7, "targetRotationOffset": 90, "levelId": 406, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-406.json"}, "rollSequence": ["E", "S", "W", "E", "S", "E", "S", "S", "S", "W"], "observedPathFaces": [{"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "W", "E", "S", "E", "S", "S", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "P", "rotation": 180}, "FRONT": {"patternId": "Y", "rotation": 0}, "RIGHT": {"patternId": "X", "rotation": 0}, "BACK": {"patternId": "L", "rotation": 180}, "LEFT": {"patternId": "Y", "rotation": 270}, "BOTTOM": {"patternId": "C", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C406\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=Y, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=L, rotation=180]\n[LEFT: patternId=Y, rotation=270] [TOP: patternId=P, rotation=180] [RIGHT: patternId=X, rotation=0]\n [FRONT: patternId=Y, rotation=0]\n [BOTTOM: patternId=C, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=L, rotation=180\n- LEFT: patternId=Y, rotation=270\n- TOP: patternId=P, rotation=180\n- RIGHT: patternId=X, rotation=0\n- FRONT: patternId=Y, rotation=0\n- BOTTOM: patternId=C, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C406/initial_net.png", "targetTopFaceImage": "images/C406/target_top_face.png"}, "__sample_id__": "C406"} +{"taskType": "roll_to_target_top_face", "code": "C407", "name": "Goal Roll C407", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "8", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "U", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "S", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "B", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_down", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "2", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "8", "rotation": 0}, "FRONT": {"patternId": "U", "rotation": 180}, "RIGHT": {"patternId": "S", "rotation": 90}, "BACK": {"patternId": "B", "rotation": 180}, "LEFT": {"patternId": "arrow_down", "rotation": 90}, "BOTTOM": {"patternId": "2", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "S", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C407/initial_net.png", "targetTopFaceImage": "../images/C407/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 407, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-407.json"}, "rollSequence": ["W", "W", "N", "S", "W", "S", "W", "S", "W", "N"], "observedPathFaces": [{"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "N", "S", "W", "S", "W", "S", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "8", "rotation": 0}, "FRONT": {"patternId": "U", "rotation": 180}, "RIGHT": {"patternId": "S", "rotation": 90}, "BACK": {"patternId": "B", "rotation": 180}, "LEFT": {"patternId": "arrow_down", "rotation": 90}, "BOTTOM": {"patternId": "2", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C407\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=S, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=B, rotation=180]\n[LEFT: patternId=arrow_down, rotation=90] [TOP: patternId=8, rotation=0] [RIGHT: patternId=S, rotation=90]\n [FRONT: patternId=U, rotation=180]\n [BOTTOM: patternId=2, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=B, rotation=180\n- LEFT: patternId=arrow_down, rotation=90\n- TOP: patternId=8, rotation=0\n- RIGHT: patternId=S, rotation=90\n- FRONT: patternId=U, rotation=180\n- BOTTOM: patternId=2, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C407/initial_net.png", "targetTopFaceImage": "images/C407/target_top_face.png"}, "__sample_id__": "C407"} +{"taskType": "roll_to_target_top_face", "code": "C408", "name": "Goal Roll C408", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "2", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "M", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "L", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "Z", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "Q", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "A", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "2", "rotation": 180}, "FRONT": {"patternId": "M", "rotation": 270}, "RIGHT": {"patternId": "L", "rotation": 180}, "BACK": {"patternId": "Z", "rotation": 270}, "LEFT": {"patternId": "Q", "rotation": 90}, "BOTTOM": {"patternId": "A", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 8, "stepNumber": 9, "patternId": "Q", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C408/initial_net.png", "targetTopFaceImage": "../images/C408/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 9, "targetRotationOffset": 90, "levelId": 408, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-408.json"}, "rollSequence": ["S", "W", "S", "S", "W", "N", "W", "S", "S", "W"], "observedPathFaces": [{"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "S", "S", "W", "N", "W", "S", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "2", "rotation": 180}, "FRONT": {"patternId": "M", "rotation": 270}, "RIGHT": {"patternId": "L", "rotation": 180}, "BACK": {"patternId": "Z", "rotation": 270}, "LEFT": {"patternId": "Q", "rotation": 90}, "BOTTOM": {"patternId": "A", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C408\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=Q, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=Z, rotation=270]\n[LEFT: patternId=Q, rotation=90] [TOP: patternId=2, rotation=180] [RIGHT: patternId=L, rotation=180]\n [FRONT: patternId=M, rotation=270]\n [BOTTOM: patternId=A, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Z, rotation=270\n- LEFT: patternId=Q, rotation=90\n- TOP: patternId=2, rotation=180\n- RIGHT: patternId=L, rotation=180\n- FRONT: patternId=M, rotation=270\n- BOTTOM: patternId=A, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C408/initial_net.png", "targetTopFaceImage": "images/C408/target_top_face.png"}, "__sample_id__": "C408"} +{"taskType": "roll_to_target_top_face", "code": "C409", "name": "Goal Roll C409", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "N", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "V", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "P", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "A", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "M", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "K", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "N", "rotation": 180}, "FRONT": {"patternId": "V", "rotation": 270}, "RIGHT": {"patternId": "P", "rotation": 0}, "BACK": {"patternId": "A", "rotation": 180}, "LEFT": {"patternId": "M", "rotation": 180}, "BOTTOM": {"patternId": "K", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "K", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C409/initial_net.png", "targetTopFaceImage": "../images/C409/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 6, "targetRotationOffset": 180, "levelId": 409, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-409.json"}, "rollSequence": ["N", "W", "S", "E", "S", "E", "E", "S", "S", "E"], "observedPathFaces": [{"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "S", "E", "S", "E", "E", "S", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "N", "rotation": 180}, "FRONT": {"patternId": "V", "rotation": 270}, "RIGHT": {"patternId": "P", "rotation": 0}, "BACK": {"patternId": "A", "rotation": 180}, "LEFT": {"patternId": "M", "rotation": 180}, "BOTTOM": {"patternId": "K", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C409\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=K, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=A, rotation=180]\n[LEFT: patternId=M, rotation=180] [TOP: patternId=N, rotation=180] [RIGHT: patternId=P, rotation=0]\n [FRONT: patternId=V, rotation=270]\n [BOTTOM: patternId=K, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=A, rotation=180\n- LEFT: patternId=M, rotation=180\n- TOP: patternId=N, rotation=180\n- RIGHT: patternId=P, rotation=0\n- FRONT: patternId=V, rotation=270\n- BOTTOM: patternId=K, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C409/initial_net.png", "targetTopFaceImage": "images/C409/target_top_face.png"}, "__sample_id__": "C409"} +{"taskType": "roll_to_target_top_face", "code": "C410", "name": "Goal Roll C410", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "3", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "B", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "A", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "4", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "C", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "circle", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "3", "rotation": 0}, "FRONT": {"patternId": "B", "rotation": 270}, "RIGHT": {"patternId": "A", "rotation": 90}, "BACK": {"patternId": "4", "rotation": 180}, "LEFT": {"patternId": "C", "rotation": 270}, "BOTTOM": {"patternId": "circle", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "circle", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C410/initial_net.png", "targetTopFaceImage": "../images/C410/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 2, "targetRotationOffset": 90, "levelId": 410, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-410.json"}, "rollSequence": ["N", "N", "E", "E", "E", "S", "S", "S", "N", "W"], "observedPathFaces": [{"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "E", "E", "E", "S", "S", "S", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "3", "rotation": 0}, "FRONT": {"patternId": "B", "rotation": 270}, "RIGHT": {"patternId": "A", "rotation": 90}, "BACK": {"patternId": "4", "rotation": 180}, "LEFT": {"patternId": "C", "rotation": 270}, "BOTTOM": {"patternId": "circle", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C410\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=circle, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=4, rotation=180]\n[LEFT: patternId=C, rotation=270] [TOP: patternId=3, rotation=0] [RIGHT: patternId=A, rotation=90]\n [FRONT: patternId=B, rotation=270]\n [BOTTOM: patternId=circle, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=4, rotation=180\n- LEFT: patternId=C, rotation=270\n- TOP: patternId=3, rotation=0\n- RIGHT: patternId=A, rotation=90\n- FRONT: patternId=B, rotation=270\n- BOTTOM: patternId=circle, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C410/initial_net.png", "targetTopFaceImage": "images/C410/target_top_face.png"}, "__sample_id__": "C410"} +{"taskType": "roll_to_target_top_face", "code": "C411", "name": "Goal Roll C411", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "W", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "O", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "heart", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "6", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_up", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "Z", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "W", "rotation": 180}, "FRONT": {"patternId": "O", "rotation": 90}, "RIGHT": {"patternId": "heart", "rotation": 180}, "BACK": {"patternId": "6", "rotation": 90}, "LEFT": {"patternId": "arrow_up", "rotation": 90}, "BOTTOM": {"patternId": "Z", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "arrow_up", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C411/initial_net.png", "targetTopFaceImage": "../images/C411/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 4, "targetRotationOffset": 270, "levelId": 411, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-411.json"}, "rollSequence": ["W", "E", "S", "E", "S", "W", "S", "W", "S", "N"], "observedPathFaces": [{"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "E", "S", "E", "S", "W", "S", "W", "S", "N"]}, "legacy_answer": {"TOP": {"patternId": "W", "rotation": 180}, "FRONT": {"patternId": "O", "rotation": 90}, "RIGHT": {"patternId": "heart", "rotation": 180}, "BACK": {"patternId": "6", "rotation": 90}, "LEFT": {"patternId": "arrow_up", "rotation": 90}, "BOTTOM": {"patternId": "Z", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C411\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=arrow_up, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=6, rotation=90]\n[LEFT: patternId=arrow_up, rotation=90] [TOP: patternId=W, rotation=180] [RIGHT: patternId=heart, rotation=180]\n [FRONT: patternId=O, rotation=90]\n [BOTTOM: patternId=Z, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=6, rotation=90\n- LEFT: patternId=arrow_up, rotation=90\n- TOP: patternId=W, rotation=180\n- RIGHT: patternId=heart, rotation=180\n- FRONT: patternId=O, rotation=90\n- BOTTOM: patternId=Z, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C411/initial_net.png", "targetTopFaceImage": "images/C411/target_top_face.png"}, "__sample_id__": "C411"} +{"taskType": "roll_to_target_top_face", "code": "C412", "name": "Goal Roll C412", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "U", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "S", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "1", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_up", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "1", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_right", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "U", "rotation": 90}, "FRONT": {"patternId": "S", "rotation": 180}, "RIGHT": {"patternId": "1", "rotation": 0}, "BACK": {"patternId": "arrow_up", "rotation": 90}, "LEFT": {"patternId": "1", "rotation": 90}, "BOTTOM": {"patternId": "arrow_right", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "1", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C412/initial_net.png", "targetTopFaceImage": "../images/C412/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 2, "targetRotationOffset": 180, "levelId": 412, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-412.json"}, "rollSequence": ["N", "E", "E", "E", "S", "W", "W", "W", "N", "S"], "observedPathFaces": [{"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "E", "E", "S", "W", "W", "W", "N", "S"]}, "legacy_answer": {"TOP": {"patternId": "U", "rotation": 90}, "FRONT": {"patternId": "S", "rotation": 180}, "RIGHT": {"patternId": "1", "rotation": 0}, "BACK": {"patternId": "arrow_up", "rotation": 90}, "LEFT": {"patternId": "1", "rotation": 90}, "BOTTOM": {"patternId": "arrow_right", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C412\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=1, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_up, rotation=90]\n[LEFT: patternId=1, rotation=90] [TOP: patternId=U, rotation=90] [RIGHT: patternId=1, rotation=0]\n [FRONT: patternId=S, rotation=180]\n [BOTTOM: patternId=arrow_right, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_up, rotation=90\n- LEFT: patternId=1, rotation=90\n- TOP: patternId=U, rotation=90\n- RIGHT: patternId=1, rotation=0\n- FRONT: patternId=S, rotation=180\n- BOTTOM: patternId=arrow_right, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C412/initial_net.png", "targetTopFaceImage": "images/C412/target_top_face.png"}, "__sample_id__": "C412"} +{"taskType": "roll_to_target_top_face", "code": "C413", "name": "Goal Roll C413", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "O", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "5", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "5", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "circle", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_left", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "1", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "O", "rotation": 180}, "FRONT": {"patternId": "5", "rotation": 90}, "RIGHT": {"patternId": "5", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 270}, "LEFT": {"patternId": "arrow_left", "rotation": 90}, "BOTTOM": {"patternId": "1", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "1", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C413/initial_net.png", "targetTopFaceImage": "../images/C413/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 6, "targetRotationOffset": 180, "levelId": 413, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-413.json"}, "rollSequence": ["S", "W", "N", "N", "W", "N", "N", "W", "E", "S"], "observedPathFaces": [{"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "N", "N", "W", "N", "N", "W", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 180}, "FRONT": {"patternId": "5", "rotation": 90}, "RIGHT": {"patternId": "5", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 270}, "LEFT": {"patternId": "arrow_left", "rotation": 90}, "BOTTOM": {"patternId": "1", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C413\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=1, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=circle, rotation=270]\n[LEFT: patternId=arrow_left, rotation=90] [TOP: patternId=O, rotation=180] [RIGHT: patternId=5, rotation=0]\n [FRONT: patternId=5, rotation=90]\n [BOTTOM: patternId=1, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=circle, rotation=270\n- LEFT: patternId=arrow_left, rotation=90\n- TOP: patternId=O, rotation=180\n- RIGHT: patternId=5, rotation=0\n- FRONT: patternId=5, rotation=90\n- BOTTOM: patternId=1, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C413/initial_net.png", "targetTopFaceImage": "images/C413/target_top_face.png"}, "__sample_id__": "C413"} +{"taskType": "roll_to_target_top_face", "code": "C414", "name": "Goal Roll C414", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "B", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "triangle", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "star", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "star", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "plus", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "9", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "B", "rotation": 270}, "FRONT": {"patternId": "triangle", "rotation": 180}, "RIGHT": {"patternId": "star", "rotation": 180}, "BACK": {"patternId": "star", "rotation": 180}, "LEFT": {"patternId": "plus", "rotation": 180}, "BOTTOM": {"patternId": "9", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 9, "stepNumber": 10, "patternId": "B", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C414/initial_net.png", "targetTopFaceImage": "../images/C414/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 10, "targetRotationOffset": 90, "levelId": 414, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-414.json"}, "rollSequence": ["W", "N", "W", "W", "S", "S", "N", "E", "E", "E"], "observedPathFaces": [{"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "W", "W", "S", "S", "N", "E", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "B", "rotation": 270}, "FRONT": {"patternId": "triangle", "rotation": 180}, "RIGHT": {"patternId": "star", "rotation": 180}, "BACK": {"patternId": "star", "rotation": 180}, "LEFT": {"patternId": "plus", "rotation": 180}, "BOTTOM": {"patternId": "9", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C414\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=B, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=star, rotation=180]\n[LEFT: patternId=plus, rotation=180] [TOP: patternId=B, rotation=270] [RIGHT: patternId=star, rotation=180]\n [FRONT: patternId=triangle, rotation=180]\n [BOTTOM: patternId=9, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=star, rotation=180\n- LEFT: patternId=plus, rotation=180\n- TOP: patternId=B, rotation=270\n- RIGHT: patternId=star, rotation=180\n- FRONT: patternId=triangle, rotation=180\n- BOTTOM: patternId=9, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C414/initial_net.png", "targetTopFaceImage": "images/C414/target_top_face.png"}, "__sample_id__": "C414"} +{"taskType": "roll_to_target_top_face", "code": "C415", "name": "Goal Roll C415", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "smile", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "G", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "8", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "Y", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_down", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "P", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "smile", "rotation": 270}, "FRONT": {"patternId": "G", "rotation": 90}, "RIGHT": {"patternId": "8", "rotation": 270}, "BACK": {"patternId": "Y", "rotation": 270}, "LEFT": {"patternId": "arrow_down", "rotation": 180}, "BOTTOM": {"patternId": "P", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "8", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C415/initial_net.png", "targetTopFaceImage": "../images/C415/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 5, "targetRotationOffset": 90, "levelId": 415, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-415.json"}, "rollSequence": ["S", "S", "E", "S", "S", "N", "W", "W", "N", "W"], "observedPathFaces": [{"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "E", "S", "S", "N", "W", "W", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "smile", "rotation": 270}, "FRONT": {"patternId": "G", "rotation": 90}, "RIGHT": {"patternId": "8", "rotation": 270}, "BACK": {"patternId": "Y", "rotation": 270}, "LEFT": {"patternId": "arrow_down", "rotation": 180}, "BOTTOM": {"patternId": "P", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C415\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=8, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=Y, rotation=270]\n[LEFT: patternId=arrow_down, rotation=180] [TOP: patternId=smile, rotation=270] [RIGHT: patternId=8, rotation=270]\n [FRONT: patternId=G, rotation=90]\n [BOTTOM: patternId=P, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Y, rotation=270\n- LEFT: patternId=arrow_down, rotation=180\n- TOP: patternId=smile, rotation=270\n- RIGHT: patternId=8, rotation=270\n- FRONT: patternId=G, rotation=90\n- BOTTOM: patternId=P, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C415/initial_net.png", "targetTopFaceImage": "images/C415/target_top_face.png"}, "__sample_id__": "C415"} +{"taskType": "roll_to_target_top_face", "code": "C416", "name": "Goal Roll C416", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "G", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "plus", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "smile", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_down", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "6", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "G", "rotation": 180}, "FRONT": {"patternId": "plus", "rotation": 270}, "RIGHT": {"patternId": "smile", "rotation": 180}, "BACK": {"patternId": "arrow_down", "rotation": 180}, "LEFT": {"patternId": "6", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "smile", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C416/initial_net.png", "targetTopFaceImage": "../images/C416/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 4, "targetRotationOffset": 270, "levelId": 416, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-416.json"}, "rollSequence": ["S", "W", "S", "N", "W", "W", "W", "E", "E", "S"], "observedPathFaces": [{"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "S", "N", "W", "W", "W", "E", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "G", "rotation": 180}, "FRONT": {"patternId": "plus", "rotation": 270}, "RIGHT": {"patternId": "smile", "rotation": 180}, "BACK": {"patternId": "arrow_down", "rotation": 180}, "LEFT": {"patternId": "6", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C416\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=smile, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_down, rotation=180]\n[LEFT: patternId=6, rotation=90] [TOP: patternId=G, rotation=180] [RIGHT: patternId=smile, rotation=180]\n [FRONT: patternId=plus, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_down, rotation=180\n- LEFT: patternId=6, rotation=90\n- TOP: patternId=G, rotation=180\n- RIGHT: patternId=smile, rotation=180\n- FRONT: patternId=plus, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C416/initial_net.png", "targetTopFaceImage": "images/C416/target_top_face.png"}, "__sample_id__": "C416"} +{"taskType": "roll_to_target_top_face", "code": "C417", "name": "Goal Roll C417", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "K", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "heart", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "4", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "Z", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "square", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "K", "rotation": 90}, "FRONT": {"patternId": "heart", "rotation": 180}, "RIGHT": {"patternId": "4", "rotation": 270}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "square", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 6, "stepNumber": 7, "patternId": "heart", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C417/initial_net.png", "targetTopFaceImage": "../images/C417/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 7, "targetRotationOffset": 270, "levelId": 417, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-417.json"}, "rollSequence": ["N", "E", "S", "E", "E", "N", "E", "N", "W", "W"], "observedPathFaces": [{"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "S", "E", "E", "N", "E", "N", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "K", "rotation": 90}, "FRONT": {"patternId": "heart", "rotation": 180}, "RIGHT": {"patternId": "4", "rotation": 270}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "square", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C417\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=heart, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=Z, rotation=90]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=K, rotation=90] [RIGHT: patternId=4, rotation=270]\n [FRONT: patternId=heart, rotation=180]\n [BOTTOM: patternId=square, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Z, rotation=90\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=K, rotation=90\n- RIGHT: patternId=4, rotation=270\n- FRONT: patternId=heart, rotation=180\n- BOTTOM: patternId=square, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C417/initial_net.png", "targetTopFaceImage": "images/C417/target_top_face.png"}, "__sample_id__": "C417"} +{"taskType": "roll_to_target_top_face", "code": "C418", "name": "Goal Roll C418", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "plus", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "N", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "J", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "1", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_right", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "plus", "rotation": 180}, "FRONT": {"patternId": "N", "rotation": 90}, "RIGHT": {"patternId": "J", "rotation": 0}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_right", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "arrow_right", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C418/initial_net.png", "targetTopFaceImage": "../images/C418/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 2, "targetRotationOffset": 270, "levelId": 418, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-418.json"}, "rollSequence": ["E", "E", "S", "W", "E", "S", "W", "N", "W", "W"], "observedPathFaces": [{"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "S", "W", "E", "S", "W", "N", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "plus", "rotation": 180}, "FRONT": {"patternId": "N", "rotation": 90}, "RIGHT": {"patternId": "J", "rotation": 0}, "BACK": {"patternId": "1", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "arrow_right", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C418\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=arrow_right, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=1, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=plus, rotation=180] [RIGHT: patternId=J, rotation=0]\n [FRONT: patternId=N, rotation=90]\n [BOTTOM: patternId=arrow_right, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=1, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=plus, rotation=180\n- RIGHT: patternId=J, rotation=0\n- FRONT: patternId=N, rotation=90\n- BOTTOM: patternId=arrow_right, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C418/initial_net.png", "targetTopFaceImage": "images/C418/target_top_face.png"}, "__sample_id__": "C418"} +{"taskType": "roll_to_target_top_face", "code": "C419", "name": "Goal Roll C419", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "5", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "H", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "2", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "3", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "R", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "5", "rotation": 270}, "FRONT": {"patternId": "H", "rotation": 90}, "RIGHT": {"patternId": "2", "rotation": 270}, "BACK": {"patternId": "3", "rotation": 90}, "LEFT": {"patternId": "R", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 6, "stepNumber": 7, "patternId": "H", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C419/initial_net.png", "targetTopFaceImage": "../images/C419/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 7, "targetRotationOffset": 180, "levelId": 419, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-419.json"}, "rollSequence": ["S", "E", "S", "W", "S", "E", "S", "E", "E", "N"], "observedPathFaces": [{"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "S", "W", "S", "E", "S", "E", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "5", "rotation": 270}, "FRONT": {"patternId": "H", "rotation": 90}, "RIGHT": {"patternId": "2", "rotation": 270}, "BACK": {"patternId": "3", "rotation": 90}, "LEFT": {"patternId": "R", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C419\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=H, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=3, rotation=90]\n[LEFT: patternId=R, rotation=90] [TOP: patternId=5, rotation=270] [RIGHT: patternId=2, rotation=270]\n [FRONT: patternId=H, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=3, rotation=90\n- LEFT: patternId=R, rotation=90\n- TOP: patternId=5, rotation=270\n- RIGHT: patternId=2, rotation=270\n- FRONT: patternId=H, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C419/initial_net.png", "targetTopFaceImage": "images/C419/target_top_face.png"}, "__sample_id__": "C419"} +{"taskType": "roll_to_target_top_face", "code": "C420", "name": "Goal Roll C420", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "H", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "I", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "K", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "I", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "8", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 180}, "RIGHT": {"patternId": "I", "rotation": 180}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "I", "rotation": 270}, "BOTTOM": {"patternId": "8", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "I", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C420/initial_net.png", "targetTopFaceImage": "../images/C420/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 5, "targetRotationOffset": 270, "levelId": 420, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-420.json"}, "rollSequence": ["E", "N", "W", "W", "N", "E", "N", "E", "S", "E"], "observedPathFaces": [{"patternId": "I", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "W", "W", "N", "E", "N", "E", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 180}, "RIGHT": {"patternId": "I", "rotation": 180}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "I", "rotation": 270}, "BOTTOM": {"patternId": "8", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C420\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=I, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=K, rotation=270]\n[LEFT: patternId=I, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=I, rotation=180]\n [FRONT: patternId=H, rotation=180]\n [BOTTOM: patternId=8, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=K, rotation=270\n- LEFT: patternId=I, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=I, rotation=180\n- FRONT: patternId=H, rotation=180\n- BOTTOM: patternId=8, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C420/initial_net.png", "targetTopFaceImage": "images/C420/target_top_face.png"}, "__sample_id__": "C420"} +{"taskType": "roll_to_target_top_face", "code": "C421", "name": "Goal Roll C421", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "V", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "C", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "M", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "3", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "W", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "V", "rotation": 0}, "RIGHT": {"patternId": "C", "rotation": 270}, "BACK": {"patternId": "M", "rotation": 90}, "LEFT": {"patternId": "3", "rotation": 270}, "BOTTOM": {"patternId": "W", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 9, "stepNumber": 10, "patternId": "V", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C421/initial_net.png", "targetTopFaceImage": "../images/C421/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 10, "targetRotationOffset": 270, "levelId": 421, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-421.json"}, "rollSequence": ["E", "W", "S", "E", "W", "E", "N", "W", "N", "N"], "observedPathFaces": [{"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "W", "S", "E", "W", "E", "N", "W", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "V", "rotation": 0}, "RIGHT": {"patternId": "C", "rotation": 270}, "BACK": {"patternId": "M", "rotation": 90}, "LEFT": {"patternId": "3", "rotation": 270}, "BOTTOM": {"patternId": "W", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C421\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=V, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=M, rotation=90]\n[LEFT: patternId=3, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=C, rotation=270]\n [FRONT: patternId=V, rotation=0]\n [BOTTOM: patternId=W, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=M, rotation=90\n- LEFT: patternId=3, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=C, rotation=270\n- FRONT: patternId=V, rotation=0\n- BOTTOM: patternId=W, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C421/initial_net.png", "targetTopFaceImage": "images/C421/target_top_face.png"}, "__sample_id__": "C421"} +{"taskType": "roll_to_target_top_face", "code": "C422", "name": "Goal Roll C422", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "5", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "H", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "E", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "circle", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "V", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "1", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "5", "rotation": 90}, "FRONT": {"patternId": "H", "rotation": 0}, "RIGHT": {"patternId": "E", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 270}, "LEFT": {"patternId": "V", "rotation": 90}, "BOTTOM": {"patternId": "1", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 6, "stepNumber": 7, "patternId": "1", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C422/initial_net.png", "targetTopFaceImage": "../images/C422/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 7, "targetRotationOffset": 90, "levelId": 422, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-422.json"}, "rollSequence": ["E", "E", "N", "W", "W", "W", "S", "S", "W", "S"], "observedPathFaces": [{"patternId": "E", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "N", "W", "W", "W", "S", "S", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "5", "rotation": 90}, "FRONT": {"patternId": "H", "rotation": 0}, "RIGHT": {"patternId": "E", "rotation": 0}, "BACK": {"patternId": "circle", "rotation": 270}, "LEFT": {"patternId": "V", "rotation": 90}, "BOTTOM": {"patternId": "1", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C422\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=1, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=circle, rotation=270]\n[LEFT: patternId=V, rotation=90] [TOP: patternId=5, rotation=90] [RIGHT: patternId=E, rotation=0]\n [FRONT: patternId=H, rotation=0]\n [BOTTOM: patternId=1, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=circle, rotation=270\n- LEFT: patternId=V, rotation=90\n- TOP: patternId=5, rotation=90\n- RIGHT: patternId=E, rotation=0\n- FRONT: patternId=H, rotation=0\n- BOTTOM: patternId=1, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C422/initial_net.png", "targetTopFaceImage": "images/C422/target_top_face.png"}, "__sample_id__": "C422"} +{"taskType": "roll_to_target_top_face", "code": "C423", "name": "Goal Roll C423", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "B", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "heart", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "F", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "M", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "F", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "B", "rotation": 270}, "FRONT": {"patternId": "heart", "rotation": 270}, "RIGHT": {"patternId": "F", "rotation": 90}, "BACK": {"patternId": "M", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "F", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "B", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C423/initial_net.png", "targetTopFaceImage": "../images/C423/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 3, "targetRotationOffset": 270, "levelId": 423, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-423.json"}, "rollSequence": ["S", "E", "N", "E", "S", "E", "N", "W", "N", "E"], "observedPathFaces": [{"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "N", "E", "S", "E", "N", "W", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "B", "rotation": 270}, "FRONT": {"patternId": "heart", "rotation": 270}, "RIGHT": {"patternId": "F", "rotation": 90}, "BACK": {"patternId": "M", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "F", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C423\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=B, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=M, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=B, rotation=270] [RIGHT: patternId=F, rotation=90]\n [FRONT: patternId=heart, rotation=270]\n [BOTTOM: patternId=F, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=M, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=B, rotation=270\n- RIGHT: patternId=F, rotation=90\n- FRONT: patternId=heart, rotation=270\n- BOTTOM: patternId=F, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C423/initial_net.png", "targetTopFaceImage": "images/C423/target_top_face.png"}, "__sample_id__": "C423"} +{"taskType": "roll_to_target_top_face", "code": "C424", "name": "Goal Roll C424", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "A", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "Z", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "U", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "diamond", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "D", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "heart", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "A", "rotation": 90}, "FRONT": {"patternId": "Z", "rotation": 0}, "RIGHT": {"patternId": "U", "rotation": 0}, "BACK": {"patternId": "diamond", "rotation": 270}, "LEFT": {"patternId": "D", "rotation": 180}, "BOTTOM": {"patternId": "heart", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "D", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C424/initial_net.png", "targetTopFaceImage": "../images/C424/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 3, "targetRotationOffset": 180, "levelId": 424, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-424.json"}, "rollSequence": ["W", "N", "N", "E", "N", "E", "E", "N", "E", "N"], "observedPathFaces": [{"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "N", "E", "N", "E", "E", "N", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "A", "rotation": 90}, "FRONT": {"patternId": "Z", "rotation": 0}, "RIGHT": {"patternId": "U", "rotation": 0}, "BACK": {"patternId": "diamond", "rotation": 270}, "LEFT": {"patternId": "D", "rotation": 180}, "BOTTOM": {"patternId": "heart", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C424\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=D, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=diamond, rotation=270]\n[LEFT: patternId=D, rotation=180] [TOP: patternId=A, rotation=90] [RIGHT: patternId=U, rotation=0]\n [FRONT: patternId=Z, rotation=0]\n [BOTTOM: patternId=heart, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=diamond, rotation=270\n- LEFT: patternId=D, rotation=180\n- TOP: patternId=A, rotation=90\n- RIGHT: patternId=U, rotation=0\n- FRONT: patternId=Z, rotation=0\n- BOTTOM: patternId=heart, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C424/initial_net.png", "targetTopFaceImage": "images/C424/target_top_face.png"}, "__sample_id__": "C424"} +{"taskType": "roll_to_target_top_face", "code": "C425", "name": "Goal Roll C425", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "I", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "4", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "3", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "I", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "7", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "I", "rotation": 90}, "FRONT": {"patternId": "4", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "3", "rotation": 180}, "LEFT": {"patternId": "I", "rotation": 180}, "BOTTOM": {"patternId": "7", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 6, "stepNumber": 7, "patternId": "4", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C425/initial_net.png", "targetTopFaceImage": "../images/C425/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 7, "targetRotationOffset": 270, "levelId": 425, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-425.json"}, "rollSequence": ["S", "W", "W", "E", "E", "N", "N", "N", "W", "S"], "observedPathFaces": [{"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "W", "E", "E", "N", "N", "N", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "I", "rotation": 90}, "FRONT": {"patternId": "4", "rotation": 90}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "3", "rotation": 180}, "LEFT": {"patternId": "I", "rotation": 180}, "BOTTOM": {"patternId": "7", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C425\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=4, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=3, rotation=180]\n[LEFT: patternId=I, rotation=180] [TOP: patternId=I, rotation=90] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=4, rotation=90]\n [BOTTOM: patternId=7, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=3, rotation=180\n- LEFT: patternId=I, rotation=180\n- TOP: patternId=I, rotation=90\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=4, rotation=90\n- BOTTOM: patternId=7, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C425/initial_net.png", "targetTopFaceImage": "images/C425/target_top_face.png"}, "__sample_id__": "C425"} +{"taskType": "roll_to_target_top_face", "code": "C426", "name": "Goal Roll C426", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "triangle", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "F", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "X", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "star", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "9", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "heart", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "triangle", "rotation": 270}, "FRONT": {"patternId": "F", "rotation": 270}, "RIGHT": {"patternId": "X", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 270}, "LEFT": {"patternId": "9", "rotation": 90}, "BOTTOM": {"patternId": "heart", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "star", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C426/initial_net.png", "targetTopFaceImage": "../images/C426/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 3, "targetRotationOffset": 180, "levelId": 426, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-426.json"}, "rollSequence": ["N", "S", "S", "W", "S", "W", "S", "E", "S", "W"], "observedPathFaces": [{"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "S", "S", "W", "S", "W", "S", "E", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "triangle", "rotation": 270}, "FRONT": {"patternId": "F", "rotation": 270}, "RIGHT": {"patternId": "X", "rotation": 0}, "BACK": {"patternId": "star", "rotation": 270}, "LEFT": {"patternId": "9", "rotation": 90}, "BOTTOM": {"patternId": "heart", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C426\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=star, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=star, rotation=270]\n[LEFT: patternId=9, rotation=90] [TOP: patternId=triangle, rotation=270] [RIGHT: patternId=X, rotation=0]\n [FRONT: patternId=F, rotation=270]\n [BOTTOM: patternId=heart, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=star, rotation=270\n- LEFT: patternId=9, rotation=90\n- TOP: patternId=triangle, rotation=270\n- RIGHT: patternId=X, rotation=0\n- FRONT: patternId=F, rotation=270\n- BOTTOM: patternId=heart, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C426/initial_net.png", "targetTopFaceImage": "images/C426/target_top_face.png"}, "__sample_id__": "C426"} +{"taskType": "roll_to_target_top_face", "code": "C427", "name": "Goal Roll C427", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "X", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "star", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "E", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "X", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "B", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "D", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "X", "rotation": 90}, "FRONT": {"patternId": "star", "rotation": 0}, "RIGHT": {"patternId": "E", "rotation": 90}, "BACK": {"patternId": "X", "rotation": 90}, "LEFT": {"patternId": "B", "rotation": 270}, "BOTTOM": {"patternId": "D", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "X", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C427/initial_net.png", "targetTopFaceImage": "../images/C427/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 6, "targetRotationOffset": 90, "levelId": 427, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-427.json"}, "rollSequence": ["N", "N", "S", "E", "N", "E", "N", "N", "E", "E"], "observedPathFaces": [{"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "S", "E", "N", "E", "N", "N", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "X", "rotation": 90}, "FRONT": {"patternId": "star", "rotation": 0}, "RIGHT": {"patternId": "E", "rotation": 90}, "BACK": {"patternId": "X", "rotation": 90}, "LEFT": {"patternId": "B", "rotation": 270}, "BOTTOM": {"patternId": "D", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C427\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=X, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=X, rotation=90]\n[LEFT: patternId=B, rotation=270] [TOP: patternId=X, rotation=90] [RIGHT: patternId=E, rotation=90]\n [FRONT: patternId=star, rotation=0]\n [BOTTOM: patternId=D, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=X, rotation=90\n- LEFT: patternId=B, rotation=270\n- TOP: patternId=X, rotation=90\n- RIGHT: patternId=E, rotation=90\n- FRONT: patternId=star, rotation=0\n- BOTTOM: patternId=D, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C427/initial_net.png", "targetTopFaceImage": "images/C427/target_top_face.png"}, "__sample_id__": "C427"} +{"taskType": "roll_to_target_top_face", "code": "C428", "name": "Goal Roll C428", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "star", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "square", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "A", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "Q", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "diamond", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "R", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "star", "rotation": 180}, "FRONT": {"patternId": "square", "rotation": 270}, "RIGHT": {"patternId": "A", "rotation": 0}, "BACK": {"patternId": "Q", "rotation": 270}, "LEFT": {"patternId": "diamond", "rotation": 0}, "BOTTOM": {"patternId": "R", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 7, "stepNumber": 8, "patternId": "square", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C428/initial_net.png", "targetTopFaceImage": "../images/C428/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 8, "targetRotationOffset": 90, "levelId": 428, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-428.json"}, "rollSequence": ["S", "N", "N", "E", "N", "E", "N", "N", "W", "W"], "observedPathFaces": [{"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "N", "N", "E", "N", "E", "N", "N", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "star", "rotation": 180}, "FRONT": {"patternId": "square", "rotation": 270}, "RIGHT": {"patternId": "A", "rotation": 0}, "BACK": {"patternId": "Q", "rotation": 270}, "LEFT": {"patternId": "diamond", "rotation": 0}, "BOTTOM": {"patternId": "R", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C428\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=square, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=Q, rotation=270]\n[LEFT: patternId=diamond, rotation=0] [TOP: patternId=star, rotation=180] [RIGHT: patternId=A, rotation=0]\n [FRONT: patternId=square, rotation=270]\n [BOTTOM: patternId=R, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Q, rotation=270\n- LEFT: patternId=diamond, rotation=0\n- TOP: patternId=star, rotation=180\n- RIGHT: patternId=A, rotation=0\n- FRONT: patternId=square, rotation=270\n- BOTTOM: patternId=R, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C428/initial_net.png", "targetTopFaceImage": "images/C428/target_top_face.png"}, "__sample_id__": "C428"} +{"taskType": "roll_to_target_top_face", "code": "C429", "name": "Goal Roll C429", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "6", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "P", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "6", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "E", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "circle", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "E", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "6", "rotation": 270}, "FRONT": {"patternId": "P", "rotation": 90}, "RIGHT": {"patternId": "6", "rotation": 180}, "BACK": {"patternId": "E", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 0}, "BOTTOM": {"patternId": "E", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "E", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C429/initial_net.png", "targetTopFaceImage": "../images/C429/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 4, "targetRotationOffset": 270, "levelId": 429, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-429.json"}, "rollSequence": ["W", "N", "N", "W", "N", "N", "S", "N", "S", "E"], "observedPathFaces": [{"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "N", "W", "N", "N", "S", "N", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "6", "rotation": 270}, "FRONT": {"patternId": "P", "rotation": 90}, "RIGHT": {"patternId": "6", "rotation": 180}, "BACK": {"patternId": "E", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 0}, "BOTTOM": {"patternId": "E", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C429\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=E, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=E, rotation=0]\n[LEFT: patternId=circle, rotation=0] [TOP: patternId=6, rotation=270] [RIGHT: patternId=6, rotation=180]\n [FRONT: patternId=P, rotation=90]\n [BOTTOM: patternId=E, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=E, rotation=0\n- LEFT: patternId=circle, rotation=0\n- TOP: patternId=6, rotation=270\n- RIGHT: patternId=6, rotation=180\n- FRONT: patternId=P, rotation=90\n- BOTTOM: patternId=E, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C429/initial_net.png", "targetTopFaceImage": "images/C429/target_top_face.png"}, "__sample_id__": "C429"} +{"taskType": "roll_to_target_top_face", "code": "C430", "name": "Goal Roll C430", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "heart", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_up", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "9", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "smile", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "K", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "heart", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_up", "rotation": 0}, "BACK": {"patternId": "9", "rotation": 0}, "LEFT": {"patternId": "smile", "rotation": 90}, "BOTTOM": {"patternId": "K", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "smile", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C430/initial_net.png", "targetTopFaceImage": "../images/C430/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 5, "targetRotationOffset": 270, "levelId": 430, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-430.json"}, "rollSequence": ["W", "W", "N", "N", "W", "S", "E", "N", "W", "N"], "observedPathFaces": [{"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "N", "N", "W", "S", "E", "N", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "heart", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "arrow_up", "rotation": 0}, "BACK": {"patternId": "9", "rotation": 0}, "LEFT": {"patternId": "smile", "rotation": 90}, "BOTTOM": {"patternId": "K", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C430\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=smile, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=9, rotation=0]\n[LEFT: patternId=smile, rotation=90] [TOP: patternId=heart, rotation=90] [RIGHT: patternId=arrow_up, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=K, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=9, rotation=0\n- LEFT: patternId=smile, rotation=90\n- TOP: patternId=heart, rotation=90\n- RIGHT: patternId=arrow_up, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=K, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C430/initial_net.png", "targetTopFaceImage": "images/C430/target_top_face.png"}, "__sample_id__": "C430"} +{"taskType": "roll_to_target_top_face", "code": "C431", "name": "Goal Roll C431", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "9", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "arrow_left", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "heart", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "1", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "O", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "9", "rotation": 180}, "FRONT": {"patternId": "arrow_left", "rotation": 90}, "RIGHT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "1", "rotation": 90}, "BOTTOM": {"patternId": "O", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 8, "stepNumber": 9, "patternId": "1", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C431/initial_net.png", "targetTopFaceImage": "../images/C431/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 9, "targetRotationOffset": 180, "levelId": 431, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-431.json"}, "rollSequence": ["S", "N", "W", "S", "S", "W", "W", "E", "E", "N"], "observedPathFaces": [{"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "N", "W", "S", "S", "W", "W", "E", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "9", "rotation": 180}, "FRONT": {"patternId": "arrow_left", "rotation": 90}, "RIGHT": {"patternId": "heart", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "1", "rotation": 90}, "BOTTOM": {"patternId": "O", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C431\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=1, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=1, rotation=90] [TOP: patternId=9, rotation=180] [RIGHT: patternId=heart, rotation=270]\n [FRONT: patternId=arrow_left, rotation=90]\n [BOTTOM: patternId=O, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=1, rotation=90\n- TOP: patternId=9, rotation=180\n- RIGHT: patternId=heart, rotation=270\n- FRONT: patternId=arrow_left, rotation=90\n- BOTTOM: patternId=O, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C431/initial_net.png", "targetTopFaceImage": "images/C431/target_top_face.png"}, "__sample_id__": "C431"} +{"taskType": "roll_to_target_top_face", "code": "C432", "name": "Goal Roll C432", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "9", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "V", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "M", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "4", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "I", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "9", "rotation": 270}, "FRONT": {"patternId": "V", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 90}, "LEFT": {"patternId": "4", "rotation": 90}, "BOTTOM": {"patternId": "I", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "I", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C432/initial_net.png", "targetTopFaceImage": "../images/C432/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 6, "targetRotationOffset": 270, "levelId": 432, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-432.json"}, "rollSequence": ["W", "N", "W", "S", "W", "N", "S", "S", "S", "N"], "observedPathFaces": [{"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "W", "S", "W", "N", "S", "S", "S", "N"]}, "legacy_answer": {"TOP": {"patternId": "9", "rotation": 270}, "FRONT": {"patternId": "V", "rotation": 180}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "M", "rotation": 90}, "LEFT": {"patternId": "4", "rotation": 90}, "BOTTOM": {"patternId": "I", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C432\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=I, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=M, rotation=90]\n[LEFT: patternId=4, rotation=90] [TOP: patternId=9, rotation=270] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=V, rotation=180]\n [BOTTOM: patternId=I, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=M, rotation=90\n- LEFT: patternId=4, rotation=90\n- TOP: patternId=9, rotation=270\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=V, rotation=180\n- BOTTOM: patternId=I, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C432/initial_net.png", "targetTopFaceImage": "images/C432/target_top_face.png"}, "__sample_id__": "C432"} +{"taskType": "roll_to_target_top_face", "code": "C433", "name": "Goal Roll C433", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "diamond", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_up", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "S", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "1", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "diamond", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "diamond", "rotation": 180}, "RIGHT": {"patternId": "arrow_up", "rotation": 180}, "BACK": {"patternId": "S", "rotation": 90}, "LEFT": {"patternId": "1", "rotation": 90}, "BOTTOM": {"patternId": "diamond", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "1", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C433/initial_net.png", "targetTopFaceImage": "../images/C433/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 4, "targetRotationOffset": 90, "levelId": 433, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-433.json"}, "rollSequence": ["S", "N", "N", "E", "S", "E", "S", "W", "W", "N"], "observedPathFaces": [{"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "N", "N", "E", "S", "E", "S", "W", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "diamond", "rotation": 180}, "RIGHT": {"patternId": "arrow_up", "rotation": 180}, "BACK": {"patternId": "S", "rotation": 90}, "LEFT": {"patternId": "1", "rotation": 90}, "BOTTOM": {"patternId": "diamond", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C433\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=1, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=S, rotation=90]\n[LEFT: patternId=1, rotation=90] [TOP: patternId=?, rotation=0] [RIGHT: patternId=arrow_up, rotation=180]\n [FRONT: patternId=diamond, rotation=180]\n [BOTTOM: patternId=diamond, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=S, rotation=90\n- LEFT: patternId=1, rotation=90\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=arrow_up, rotation=180\n- FRONT: patternId=diamond, rotation=180\n- BOTTOM: patternId=diamond, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C433/initial_net.png", "targetTopFaceImage": "images/C433/target_top_face.png"}, "__sample_id__": "C433"} +{"taskType": "roll_to_target_top_face", "code": "C434", "name": "Goal Roll C434", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "heart", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "L", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "8", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "N", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "G", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 180}, "RIGHT": {"patternId": "L", "rotation": 90}, "BACK": {"patternId": "8", "rotation": 270}, "LEFT": {"patternId": "N", "rotation": 270}, "BOTTOM": {"patternId": "G", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 8, "stepNumber": 9, "patternId": "8", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C434/initial_net.png", "targetTopFaceImage": "../images/C434/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 9, "targetRotationOffset": 90, "levelId": 434, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-434.json"}, "rollSequence": ["E", "N", "W", "N", "W", "S", "S", "W", "W", "N"], "observedPathFaces": [{"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "W", "N", "W", "S", "S", "W", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 180}, "RIGHT": {"patternId": "L", "rotation": 90}, "BACK": {"patternId": "8", "rotation": 270}, "LEFT": {"patternId": "N", "rotation": 270}, "BOTTOM": {"patternId": "G", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C434\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=8, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=8, rotation=270]\n[LEFT: patternId=N, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=L, rotation=90]\n [FRONT: patternId=heart, rotation=180]\n [BOTTOM: patternId=G, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=8, rotation=270\n- LEFT: patternId=N, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=L, rotation=90\n- FRONT: patternId=heart, rotation=180\n- BOTTOM: patternId=G, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C434/initial_net.png", "targetTopFaceImage": "images/C434/target_top_face.png"}, "__sample_id__": "C434"} +{"taskType": "roll_to_target_top_face", "code": "C435", "name": "Goal Roll C435", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "7", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "star", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_right", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "U", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "B", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "7", "rotation": 90}, "FRONT": {"patternId": "star", "rotation": 270}, "RIGHT": {"patternId": "arrow_right", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "U", "rotation": 180}, "BOTTOM": {"patternId": "B", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 9, "stepNumber": 10, "patternId": "B", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C435/initial_net.png", "targetTopFaceImage": "../images/C435/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 10, "targetRotationOffset": 270, "levelId": 435, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-435.json"}, "rollSequence": ["S", "W", "S", "E", "E", "S", "W", "E", "W", "S"], "observedPathFaces": [{"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "S", "E", "E", "S", "W", "E", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "7", "rotation": 90}, "FRONT": {"patternId": "star", "rotation": 270}, "RIGHT": {"patternId": "arrow_right", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "U", "rotation": 180}, "BOTTOM": {"patternId": "B", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C435\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=B, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=U, rotation=180] [TOP: patternId=7, rotation=90] [RIGHT: patternId=arrow_right, rotation=270]\n [FRONT: patternId=star, rotation=270]\n [BOTTOM: patternId=B, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=U, rotation=180\n- TOP: patternId=7, rotation=90\n- RIGHT: patternId=arrow_right, rotation=270\n- FRONT: patternId=star, rotation=270\n- BOTTOM: patternId=B, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C435/initial_net.png", "targetTopFaceImage": "images/C435/target_top_face.png"}, "__sample_id__": "C435"} +{"taskType": "roll_to_target_top_face", "code": "C436", "name": "Goal Roll C436", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "8", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "4", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "E", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "5", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "heart", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "3", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "8", "rotation": 0}, "FRONT": {"patternId": "4", "rotation": 180}, "RIGHT": {"patternId": "E", "rotation": 180}, "BACK": {"patternId": "5", "rotation": 270}, "LEFT": {"patternId": "heart", "rotation": 90}, "BOTTOM": {"patternId": "3", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "heart", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C436/initial_net.png", "targetTopFaceImage": "../images/C436/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 436, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-436.json"}, "rollSequence": ["E", "S", "W", "E", "S", "S", "W", "N", "N", "S"], "observedPathFaces": [{"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "W", "E", "S", "S", "W", "N", "N", "S"]}, "legacy_answer": {"TOP": {"patternId": "8", "rotation": 0}, "FRONT": {"patternId": "4", "rotation": 180}, "RIGHT": {"patternId": "E", "rotation": 180}, "BACK": {"patternId": "5", "rotation": 270}, "LEFT": {"patternId": "heart", "rotation": 90}, "BOTTOM": {"patternId": "3", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C436\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=heart, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=5, rotation=270]\n[LEFT: patternId=heart, rotation=90] [TOP: patternId=8, rotation=0] [RIGHT: patternId=E, rotation=180]\n [FRONT: patternId=4, rotation=180]\n [BOTTOM: patternId=3, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=5, rotation=270\n- LEFT: patternId=heart, rotation=90\n- TOP: patternId=8, rotation=0\n- RIGHT: patternId=E, rotation=180\n- FRONT: patternId=4, rotation=180\n- BOTTOM: patternId=3, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C436/initial_net.png", "targetTopFaceImage": "images/C436/target_top_face.png"}, "__sample_id__": "C436"} +{"taskType": "roll_to_target_top_face", "code": "C437", "name": "Goal Roll C437", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "5", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "2", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "?", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "N", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "C", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "U", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "5", "rotation": 90}, "FRONT": {"patternId": "2", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "N", "rotation": 90}, "LEFT": {"patternId": "C", "rotation": 180}, "BOTTOM": {"patternId": "U", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "2", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C437/initial_net.png", "targetTopFaceImage": "../images/C437/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 2, "targetRotationOffset": 90, "levelId": 437, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-437.json"}, "rollSequence": ["W", "N", "W", "S", "S", "W", "W", "E", "N", "N"], "observedPathFaces": [{"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "W", "S", "S", "W", "W", "E", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "5", "rotation": 90}, "FRONT": {"patternId": "2", "rotation": 270}, "RIGHT": {"patternId": "?", "rotation": 0}, "BACK": {"patternId": "N", "rotation": 90}, "LEFT": {"patternId": "C", "rotation": 180}, "BOTTOM": {"patternId": "U", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C437\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=2, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=N, rotation=90]\n[LEFT: patternId=C, rotation=180] [TOP: patternId=5, rotation=90] [RIGHT: patternId=?, rotation=0]\n [FRONT: patternId=2, rotation=270]\n [BOTTOM: patternId=U, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=N, rotation=90\n- LEFT: patternId=C, rotation=180\n- TOP: patternId=5, rotation=90\n- RIGHT: patternId=?, rotation=0\n- FRONT: patternId=2, rotation=270\n- BOTTOM: patternId=U, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C437/initial_net.png", "targetTopFaceImage": "images/C437/target_top_face.png"}, "__sample_id__": "C437"} +{"taskType": "roll_to_target_top_face", "code": "C438", "name": "Goal Roll C438", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "T", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "L", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "smile", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "circle", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "N", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "F", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "T", "rotation": 0}, "FRONT": {"patternId": "L", "rotation": 0}, "RIGHT": {"patternId": "smile", "rotation": 90}, "BACK": {"patternId": "circle", "rotation": 180}, "LEFT": {"patternId": "N", "rotation": 180}, "BOTTOM": {"patternId": "F", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 6, "stepNumber": 7, "patternId": "F", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C438/initial_net.png", "targetTopFaceImage": "../images/C438/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 7, "targetRotationOffset": 270, "levelId": 438, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-438.json"}, "rollSequence": ["E", "S", "W", "E", "E", "S", "N", "S", "E", "N"], "observedPathFaces": [{"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "W", "E", "E", "S", "N", "S", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "T", "rotation": 0}, "FRONT": {"patternId": "L", "rotation": 0}, "RIGHT": {"patternId": "smile", "rotation": 90}, "BACK": {"patternId": "circle", "rotation": 180}, "LEFT": {"patternId": "N", "rotation": 180}, "BOTTOM": {"patternId": "F", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C438\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=F, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=circle, rotation=180]\n[LEFT: patternId=N, rotation=180] [TOP: patternId=T, rotation=0] [RIGHT: patternId=smile, rotation=90]\n [FRONT: patternId=L, rotation=0]\n [BOTTOM: patternId=F, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=circle, rotation=180\n- LEFT: patternId=N, rotation=180\n- TOP: patternId=T, rotation=0\n- RIGHT: patternId=smile, rotation=90\n- FRONT: patternId=L, rotation=0\n- BOTTOM: patternId=F, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C438/initial_net.png", "targetTopFaceImage": "images/C438/target_top_face.png"}, "__sample_id__": "C438"} +{"taskType": "roll_to_target_top_face", "code": "C439", "name": "Goal Roll C439", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "5", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "X", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "D", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_right", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "Z", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "5", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "X", "rotation": 180}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "arrow_right", "rotation": 90}, "BOTTOM": {"patternId": "Z", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 7, "stepNumber": 8, "patternId": "Z", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C439/initial_net.png", "targetTopFaceImage": "../images/C439/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 8, "targetRotationOffset": 270, "levelId": 439, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-439.json"}, "rollSequence": ["N", "N", "W", "S", "N", "W", "W", "W", "S", "E"], "observedPathFaces": [{"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "W", "S", "N", "W", "W", "W", "S", "E"]}, "legacy_answer": {"TOP": {"patternId": "5", "rotation": 90}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "X", "rotation": 180}, "BACK": {"patternId": "D", "rotation": 0}, "LEFT": {"patternId": "arrow_right", "rotation": 90}, "BOTTOM": {"patternId": "Z", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C439\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=Z, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=D, rotation=0]\n[LEFT: patternId=arrow_right, rotation=90] [TOP: patternId=5, rotation=90] [RIGHT: patternId=X, rotation=180]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=Z, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=D, rotation=0\n- LEFT: patternId=arrow_right, rotation=90\n- TOP: patternId=5, rotation=90\n- RIGHT: patternId=X, rotation=180\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=Z, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C439/initial_net.png", "targetTopFaceImage": "images/C439/target_top_face.png"}, "__sample_id__": "C439"} +{"taskType": "roll_to_target_top_face", "code": "C440", "name": "Goal Roll C440", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "T", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "arrow_up", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "A", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "W", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "star", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "T", "rotation": 90}, "FRONT": {"patternId": "arrow_up", "rotation": 90}, "RIGHT": {"patternId": "A", "rotation": 270}, "BACK": {"patternId": "W", "rotation": 180}, "LEFT": {"patternId": "star", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "arrow_up", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C440/initial_net.png", "targetTopFaceImage": "../images/C440/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 2, "targetRotationOffset": 180, "levelId": 440, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-440.json"}, "rollSequence": ["E", "N", "E", "N", "E", "E", "S", "W", "N", "N"], "observedPathFaces": [{"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "E", "N", "E", "E", "S", "W", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "T", "rotation": 90}, "FRONT": {"patternId": "arrow_up", "rotation": 90}, "RIGHT": {"patternId": "A", "rotation": 270}, "BACK": {"patternId": "W", "rotation": 180}, "LEFT": {"patternId": "star", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C440\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=arrow_up, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=W, rotation=180]\n[LEFT: patternId=star, rotation=0] [TOP: patternId=T, rotation=90] [RIGHT: patternId=A, rotation=270]\n [FRONT: patternId=arrow_up, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=W, rotation=180\n- LEFT: patternId=star, rotation=0\n- TOP: patternId=T, rotation=90\n- RIGHT: patternId=A, rotation=270\n- FRONT: patternId=arrow_up, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C440/initial_net.png", "targetTopFaceImage": "images/C440/target_top_face.png"}, "__sample_id__": "C440"} +{"taskType": "roll_to_target_top_face", "code": "C441", "name": "Goal Roll C441", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "arrow_up", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "B", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "V", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "Z", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_left", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "arrow_up", "rotation": 0}, "FRONT": {"patternId": "B", "rotation": 0}, "RIGHT": {"patternId": "V", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "Z", "rotation": 180}, "BOTTOM": {"patternId": "arrow_left", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 7, "stepNumber": 8, "patternId": "Z", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C441/initial_net.png", "targetTopFaceImage": "../images/C441/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 8, "targetRotationOffset": 90, "levelId": 441, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-441.json"}, "rollSequence": ["E", "E", "S", "S", "N", "E", "W", "W", "S", "S"], "observedPathFaces": [{"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "S", "S", "N", "E", "W", "W", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "arrow_up", "rotation": 0}, "FRONT": {"patternId": "B", "rotation": 0}, "RIGHT": {"patternId": "V", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "Z", "rotation": 180}, "BOTTOM": {"patternId": "arrow_left", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C441\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=Z, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=Z, rotation=180] [TOP: patternId=arrow_up, rotation=0] [RIGHT: patternId=V, rotation=0]\n [FRONT: patternId=B, rotation=0]\n [BOTTOM: patternId=arrow_left, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=Z, rotation=180\n- TOP: patternId=arrow_up, rotation=0\n- RIGHT: patternId=V, rotation=0\n- FRONT: patternId=B, rotation=0\n- BOTTOM: patternId=arrow_left, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C441/initial_net.png", "targetTopFaceImage": "images/C441/target_top_face.png"}, "__sample_id__": "C441"} +{"taskType": "roll_to_target_top_face", "code": "C442", "name": "Goal Roll C442", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "5", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "diamond", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "5", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "L", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "5", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_left", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "5", "rotation": 90}, "FRONT": {"patternId": "diamond", "rotation": 90}, "RIGHT": {"patternId": "5", "rotation": 90}, "BACK": {"patternId": "L", "rotation": 90}, "LEFT": {"patternId": "5", "rotation": 90}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 8, "stepNumber": 9, "patternId": "5", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C442/initial_net.png", "targetTopFaceImage": "../images/C442/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 9, "targetRotationOffset": 270, "levelId": 442, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-442.json"}, "rollSequence": ["W", "N", "W", "N", "E", "N", "E", "N", "W", "N"], "observedPathFaces": [{"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "W", "N", "E", "N", "E", "N", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "5", "rotation": 90}, "FRONT": {"patternId": "diamond", "rotation": 90}, "RIGHT": {"patternId": "5", "rotation": 90}, "BACK": {"patternId": "L", "rotation": 90}, "LEFT": {"patternId": "5", "rotation": 90}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C442\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=5, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=L, rotation=90]\n[LEFT: patternId=5, rotation=90] [TOP: patternId=5, rotation=90] [RIGHT: patternId=5, rotation=90]\n [FRONT: patternId=diamond, rotation=90]\n [BOTTOM: patternId=arrow_left, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=L, rotation=90\n- LEFT: patternId=5, rotation=90\n- TOP: patternId=5, rotation=90\n- RIGHT: patternId=5, rotation=90\n- FRONT: patternId=diamond, rotation=90\n- BOTTOM: patternId=arrow_left, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C442/initial_net.png", "targetTopFaceImage": "images/C442/target_top_face.png"}, "__sample_id__": "C442"} +{"taskType": "roll_to_target_top_face", "code": "C443", "name": "Goal Roll C443", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "P", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "K", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "G", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "circle", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "9", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "P", "rotation": 270}, "FRONT": {"patternId": "K", "rotation": 270}, "RIGHT": {"patternId": "G", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 180}, "BOTTOM": {"patternId": "9", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "9", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C443/initial_net.png", "targetTopFaceImage": "../images/C443/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 2, "targetRotationOffset": 180, "levelId": 443, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-443.json"}, "rollSequence": ["E", "E", "S", "S", "N", "E", "N", "W", "N", "E"], "observedPathFaces": [{"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "S", "S", "N", "E", "N", "W", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "P", "rotation": 270}, "FRONT": {"patternId": "K", "rotation": 270}, "RIGHT": {"patternId": "G", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 180}, "BOTTOM": {"patternId": "9", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C443\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=9, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=circle, rotation=180] [TOP: patternId=P, rotation=270] [RIGHT: patternId=G, rotation=0]\n [FRONT: patternId=K, rotation=270]\n [BOTTOM: patternId=9, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=circle, rotation=180\n- TOP: patternId=P, rotation=270\n- RIGHT: patternId=G, rotation=0\n- FRONT: patternId=K, rotation=270\n- BOTTOM: patternId=9, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C443/initial_net.png", "targetTopFaceImage": "images/C443/target_top_face.png"}, "__sample_id__": "C443"} +{"taskType": "roll_to_target_top_face", "code": "C444", "name": "Goal Roll C444", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "Z", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "arrow_right", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "D", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "8", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "1", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_left", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "Z", "rotation": 180}, "FRONT": {"patternId": "arrow_right", "rotation": 180}, "RIGHT": {"patternId": "D", "rotation": 90}, "BACK": {"patternId": "8", "rotation": 0}, "LEFT": {"patternId": "1", "rotation": 180}, "BOTTOM": {"patternId": "arrow_left", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 9, "stepNumber": 10, "patternId": "arrow_right", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C444/initial_net.png", "targetTopFaceImage": "../images/C444/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 10, "targetRotationOffset": 270, "levelId": 444, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-444.json"}, "rollSequence": ["S", "W", "W", "E", "S", "S", "N", "E", "E", "E"], "observedPathFaces": [{"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "W", "E", "S", "S", "N", "E", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "Z", "rotation": 180}, "FRONT": {"patternId": "arrow_right", "rotation": 180}, "RIGHT": {"patternId": "D", "rotation": 90}, "BACK": {"patternId": "8", "rotation": 0}, "LEFT": {"patternId": "1", "rotation": 180}, "BOTTOM": {"patternId": "arrow_left", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C444\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=arrow_right, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=8, rotation=0]\n[LEFT: patternId=1, rotation=180] [TOP: patternId=Z, rotation=180] [RIGHT: patternId=D, rotation=90]\n [FRONT: patternId=arrow_right, rotation=180]\n [BOTTOM: patternId=arrow_left, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=8, rotation=0\n- LEFT: patternId=1, rotation=180\n- TOP: patternId=Z, rotation=180\n- RIGHT: patternId=D, rotation=90\n- FRONT: patternId=arrow_right, rotation=180\n- BOTTOM: patternId=arrow_left, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C444/initial_net.png", "targetTopFaceImage": "images/C444/target_top_face.png"}, "__sample_id__": "C444"} +{"taskType": "roll_to_target_top_face", "code": "C445", "name": "Goal Roll C445", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "Q", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "F", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "R", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "smile", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "plus", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "B", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "Q", "rotation": 0}, "FRONT": {"patternId": "F", "rotation": 90}, "RIGHT": {"patternId": "R", "rotation": 0}, "BACK": {"patternId": "smile", "rotation": 90}, "LEFT": {"patternId": "plus", "rotation": 180}, "BOTTOM": {"patternId": "B", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "B", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C445/initial_net.png", "targetTopFaceImage": "../images/C445/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 2, "targetRotationOffset": 90, "levelId": 445, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-445.json"}, "rollSequence": ["S", "S", "E", "W", "W", "W", "S", "S", "W", "S"], "observedPathFaces": [{"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "E", "W", "W", "W", "S", "S", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "Q", "rotation": 0}, "FRONT": {"patternId": "F", "rotation": 90}, "RIGHT": {"patternId": "R", "rotation": 0}, "BACK": {"patternId": "smile", "rotation": 90}, "LEFT": {"patternId": "plus", "rotation": 180}, "BOTTOM": {"patternId": "B", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C445\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=B, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=smile, rotation=90]\n[LEFT: patternId=plus, rotation=180] [TOP: patternId=Q, rotation=0] [RIGHT: patternId=R, rotation=0]\n [FRONT: patternId=F, rotation=90]\n [BOTTOM: patternId=B, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=smile, rotation=90\n- LEFT: patternId=plus, rotation=180\n- TOP: patternId=Q, rotation=0\n- RIGHT: patternId=R, rotation=0\n- FRONT: patternId=F, rotation=90\n- BOTTOM: patternId=B, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C445/initial_net.png", "targetTopFaceImage": "images/C445/target_top_face.png"}, "__sample_id__": "C445"} +{"taskType": "roll_to_target_top_face", "code": "C446", "name": "Goal Roll C446", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "M", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "triangle", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "R", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "3", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_right", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "diamond", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "M", "rotation": 270}, "FRONT": {"patternId": "triangle", "rotation": 270}, "RIGHT": {"patternId": "R", "rotation": 90}, "BACK": {"patternId": "3", "rotation": 270}, "LEFT": {"patternId": "arrow_right", "rotation": 270}, "BOTTOM": {"patternId": "diamond", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "3", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C446/initial_net.png", "targetTopFaceImage": "../images/C446/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 446, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-446.json"}, "rollSequence": ["S", "W", "S", "S", "W", "S", "S", "E", "N", "W"], "observedPathFaces": [{"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "S", "S", "W", "S", "S", "E", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "M", "rotation": 270}, "FRONT": {"patternId": "triangle", "rotation": 270}, "RIGHT": {"patternId": "R", "rotation": 90}, "BACK": {"patternId": "3", "rotation": 270}, "LEFT": {"patternId": "arrow_right", "rotation": 270}, "BOTTOM": {"patternId": "diamond", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C446\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=3, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=3, rotation=270]\n[LEFT: patternId=arrow_right, rotation=270] [TOP: patternId=M, rotation=270] [RIGHT: patternId=R, rotation=90]\n [FRONT: patternId=triangle, rotation=270]\n [BOTTOM: patternId=diamond, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=3, rotation=270\n- LEFT: patternId=arrow_right, rotation=270\n- TOP: patternId=M, rotation=270\n- RIGHT: patternId=R, rotation=90\n- FRONT: patternId=triangle, rotation=270\n- BOTTOM: patternId=diamond, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C446/initial_net.png", "targetTopFaceImage": "images/C446/target_top_face.png"}, "__sample_id__": "C446"} +{"taskType": "roll_to_target_top_face", "code": "C447", "name": "Goal Roll C447", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "smile", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "W", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "L", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_left", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "Y", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_up", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "smile", "rotation": 90}, "FRONT": {"patternId": "W", "rotation": 90}, "RIGHT": {"patternId": "L", "rotation": 90}, "BACK": {"patternId": "arrow_left", "rotation": 180}, "LEFT": {"patternId": "Y", "rotation": 180}, "BOTTOM": {"patternId": "arrow_up", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "W", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C447/initial_net.png", "targetTopFaceImage": "../images/C447/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 5, "targetRotationOffset": 90, "levelId": 447, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-447.json"}, "rollSequence": ["S", "E", "E", "N", "S", "W", "W", "N", "W", "W"], "observedPathFaces": [{"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "E", "N", "S", "W", "W", "N", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "smile", "rotation": 90}, "FRONT": {"patternId": "W", "rotation": 90}, "RIGHT": {"patternId": "L", "rotation": 90}, "BACK": {"patternId": "arrow_left", "rotation": 180}, "LEFT": {"patternId": "Y", "rotation": 180}, "BOTTOM": {"patternId": "arrow_up", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C447\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=W, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_left, rotation=180]\n[LEFT: patternId=Y, rotation=180] [TOP: patternId=smile, rotation=90] [RIGHT: patternId=L, rotation=90]\n [FRONT: patternId=W, rotation=90]\n [BOTTOM: patternId=arrow_up, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_left, rotation=180\n- LEFT: patternId=Y, rotation=180\n- TOP: patternId=smile, rotation=90\n- RIGHT: patternId=L, rotation=90\n- FRONT: patternId=W, rotation=90\n- BOTTOM: patternId=arrow_up, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C447/initial_net.png", "targetTopFaceImage": "images/C447/target_top_face.png"}, "__sample_id__": "C447"} +{"taskType": "roll_to_target_top_face", "code": "C448", "name": "Goal Roll C448", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "circle", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "arrow_left", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "X", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "6", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "4", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "I", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "circle", "rotation": 0}, "FRONT": {"patternId": "arrow_left", "rotation": 0}, "RIGHT": {"patternId": "X", "rotation": 90}, "BACK": {"patternId": "6", "rotation": 0}, "LEFT": {"patternId": "4", "rotation": 270}, "BOTTOM": {"patternId": "I", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "6", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C448/initial_net.png", "targetTopFaceImage": "../images/C448/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 2, "targetRotationOffset": 90, "levelId": 448, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-448.json"}, "rollSequence": ["W", "S", "E", "S", "N", "E", "E", "S", "W", "S"], "observedPathFaces": [{"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "E", "S", "N", "E", "E", "S", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "circle", "rotation": 0}, "FRONT": {"patternId": "arrow_left", "rotation": 0}, "RIGHT": {"patternId": "X", "rotation": 90}, "BACK": {"patternId": "6", "rotation": 0}, "LEFT": {"patternId": "4", "rotation": 270}, "BOTTOM": {"patternId": "I", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C448\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=6, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=6, rotation=0]\n[LEFT: patternId=4, rotation=270] [TOP: patternId=circle, rotation=0] [RIGHT: patternId=X, rotation=90]\n [FRONT: patternId=arrow_left, rotation=0]\n [BOTTOM: patternId=I, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=6, rotation=0\n- LEFT: patternId=4, rotation=270\n- TOP: patternId=circle, rotation=0\n- RIGHT: patternId=X, rotation=90\n- FRONT: patternId=arrow_left, rotation=0\n- BOTTOM: patternId=I, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C448/initial_net.png", "targetTopFaceImage": "images/C448/target_top_face.png"}, "__sample_id__": "C448"} +{"taskType": "roll_to_target_top_face", "code": "C449", "name": "Goal Roll C449", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "square", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "star", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "smile", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "smile", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "N", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 0}, "RIGHT": {"patternId": "star", "rotation": 270}, "BACK": {"patternId": "smile", "rotation": 270}, "LEFT": {"patternId": "smile", "rotation": 270}, "BOTTOM": {"patternId": "N", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "smile", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C449/initial_net.png", "targetTopFaceImage": "../images/C449/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 2, "targetRotationOffset": 180, "levelId": 449, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-449.json"}, "rollSequence": ["E", "S", "W", "W", "E", "E", "S", "W", "N", "E"], "observedPathFaces": [{"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "W", "W", "E", "E", "S", "W", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "square", "rotation": 0}, "RIGHT": {"patternId": "star", "rotation": 270}, "BACK": {"patternId": "smile", "rotation": 270}, "LEFT": {"patternId": "smile", "rotation": 270}, "BOTTOM": {"patternId": "N", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C449\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=smile, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=smile, rotation=270]\n[LEFT: patternId=smile, rotation=270] [TOP: patternId=?, rotation=0] [RIGHT: patternId=star, rotation=270]\n [FRONT: patternId=square, rotation=0]\n [BOTTOM: patternId=N, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=smile, rotation=270\n- LEFT: patternId=smile, rotation=270\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=star, rotation=270\n- FRONT: patternId=square, rotation=0\n- BOTTOM: patternId=N, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C449/initial_net.png", "targetTopFaceImage": "images/C449/target_top_face.png"}, "__sample_id__": "C449"} +{"taskType": "roll_to_target_top_face", "code": "C450", "name": "Goal Roll C450", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "C", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "R", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Q", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "8", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "W", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "C", "rotation": 270}, "FRONT": {"patternId": "R", "rotation": 90}, "RIGHT": {"patternId": "Q", "rotation": 270}, "BACK": {"patternId": "8", "rotation": 0}, "LEFT": {"patternId": "W", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "8", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C450/initial_net.png", "targetTopFaceImage": "../images/C450/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 3, "targetRotationOffset": 90, "levelId": 450, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-450.json"}, "rollSequence": ["S", "W", "E", "S", "S", "W", "N", "W", "N", "E"], "observedPathFaces": [{"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "E", "S", "S", "W", "N", "W", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "C", "rotation": 270}, "FRONT": {"patternId": "R", "rotation": 90}, "RIGHT": {"patternId": "Q", "rotation": 270}, "BACK": {"patternId": "8", "rotation": 0}, "LEFT": {"patternId": "W", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C450\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=8, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=8, rotation=0]\n[LEFT: patternId=W, rotation=0] [TOP: patternId=C, rotation=270] [RIGHT: patternId=Q, rotation=270]\n [FRONT: patternId=R, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=8, rotation=0\n- LEFT: patternId=W, rotation=0\n- TOP: patternId=C, rotation=270\n- RIGHT: patternId=Q, rotation=270\n- FRONT: patternId=R, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C450/initial_net.png", "targetTopFaceImage": "images/C450/target_top_face.png"}, "__sample_id__": "C450"} +{"taskType": "roll_to_target_top_face", "code": "C451", "name": "Goal Roll C451", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "I", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "F", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "U", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "M", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "circle", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_down", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "I", "rotation": 270}, "FRONT": {"patternId": "F", "rotation": 270}, "RIGHT": {"patternId": "U", "rotation": 270}, "BACK": {"patternId": "M", "rotation": 90}, "LEFT": {"patternId": "circle", "rotation": 270}, "BOTTOM": {"patternId": "arrow_down", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "circle", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C451/initial_net.png", "targetTopFaceImage": "../images/C451/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 5, "targetRotationOffset": 90, "levelId": 451, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-451.json"}, "rollSequence": ["W", "W", "N", "S", "W", "E", "N", "N", "E", "N"], "observedPathFaces": [{"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "N", "S", "W", "E", "N", "N", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "I", "rotation": 270}, "FRONT": {"patternId": "F", "rotation": 270}, "RIGHT": {"patternId": "U", "rotation": 270}, "BACK": {"patternId": "M", "rotation": 90}, "LEFT": {"patternId": "circle", "rotation": 270}, "BOTTOM": {"patternId": "arrow_down", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C451\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=circle, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=M, rotation=90]\n[LEFT: patternId=circle, rotation=270] [TOP: patternId=I, rotation=270] [RIGHT: patternId=U, rotation=270]\n [FRONT: patternId=F, rotation=270]\n [BOTTOM: patternId=arrow_down, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=M, rotation=90\n- LEFT: patternId=circle, rotation=270\n- TOP: patternId=I, rotation=270\n- RIGHT: patternId=U, rotation=270\n- FRONT: patternId=F, rotation=270\n- BOTTOM: patternId=arrow_down, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C451/initial_net.png", "targetTopFaceImage": "images/C451/target_top_face.png"}, "__sample_id__": "C451"} +{"taskType": "roll_to_target_top_face", "code": "C452", "name": "Goal Roll C452", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "X", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "W", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "L", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "4", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "R", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "B", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "X", "rotation": 0}, "FRONT": {"patternId": "W", "rotation": 90}, "RIGHT": {"patternId": "L", "rotation": 180}, "BACK": {"patternId": "4", "rotation": 0}, "LEFT": {"patternId": "R", "rotation": 180}, "BOTTOM": {"patternId": "B", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 9, "stepNumber": 10, "patternId": "X", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C452/initial_net.png", "targetTopFaceImage": "../images/C452/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 10, "targetRotationOffset": 90, "levelId": 452, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-452.json"}, "rollSequence": ["S", "W", "S", "S", "E", "N", "N", "S", "W", "W"], "observedPathFaces": [{"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "S", "S", "E", "N", "N", "S", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "X", "rotation": 0}, "FRONT": {"patternId": "W", "rotation": 90}, "RIGHT": {"patternId": "L", "rotation": 180}, "BACK": {"patternId": "4", "rotation": 0}, "LEFT": {"patternId": "R", "rotation": 180}, "BOTTOM": {"patternId": "B", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C452\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=X, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=4, rotation=0]\n[LEFT: patternId=R, rotation=180] [TOP: patternId=X, rotation=0] [RIGHT: patternId=L, rotation=180]\n [FRONT: patternId=W, rotation=90]\n [BOTTOM: patternId=B, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=4, rotation=0\n- LEFT: patternId=R, rotation=180\n- TOP: patternId=X, rotation=0\n- RIGHT: patternId=L, rotation=180\n- FRONT: patternId=W, rotation=90\n- BOTTOM: patternId=B, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C452/initial_net.png", "targetTopFaceImage": "images/C452/target_top_face.png"}, "__sample_id__": "C452"} +{"taskType": "roll_to_target_top_face", "code": "C453", "name": "Goal Roll C453", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "plus", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "A", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "O", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "4", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "9", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "plus", "rotation": 90}, "FRONT": {"patternId": "A", "rotation": 270}, "RIGHT": {"patternId": "O", "rotation": 270}, "BACK": {"patternId": "4", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "9", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 6, "stepNumber": 7, "patternId": "4", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C453/initial_net.png", "targetTopFaceImage": "../images/C453/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 7, "targetRotationOffset": 90, "levelId": 453, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-453.json"}, "rollSequence": ["S", "N", "E", "W", "N", "E", "E", "S", "S", "S"], "observedPathFaces": [{"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "N", "E", "W", "N", "E", "E", "S", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "plus", "rotation": 90}, "FRONT": {"patternId": "A", "rotation": 270}, "RIGHT": {"patternId": "O", "rotation": 270}, "BACK": {"patternId": "4", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "9", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C453\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=4, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=4, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=plus, rotation=90] [RIGHT: patternId=O, rotation=270]\n [FRONT: patternId=A, rotation=270]\n [BOTTOM: patternId=9, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=4, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=plus, rotation=90\n- RIGHT: patternId=O, rotation=270\n- FRONT: patternId=A, rotation=270\n- BOTTOM: patternId=9, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C453/initial_net.png", "targetTopFaceImage": "images/C453/target_top_face.png"}, "__sample_id__": "C453"} +{"taskType": "roll_to_target_top_face", "code": "C454", "name": "Goal Roll C454", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "N", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "J", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_left", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "R", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "W", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_left", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "N", "rotation": 270}, "FRONT": {"patternId": "J", "rotation": 0}, "RIGHT": {"patternId": "arrow_left", "rotation": 90}, "BACK": {"patternId": "R", "rotation": 270}, "LEFT": {"patternId": "W", "rotation": 90}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 7, "stepNumber": 8, "patternId": "N", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C454/initial_net.png", "targetTopFaceImage": "../images/C454/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 8, "targetRotationOffset": 90, "levelId": 454, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-454.json"}, "rollSequence": ["N", "N", "E", "S", "E", "W", "S", "E", "S", "W"], "observedPathFaces": [{"patternId": "R", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "E", "S", "E", "W", "S", "E", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "N", "rotation": 270}, "FRONT": {"patternId": "J", "rotation": 0}, "RIGHT": {"patternId": "arrow_left", "rotation": 90}, "BACK": {"patternId": "R", "rotation": 270}, "LEFT": {"patternId": "W", "rotation": 90}, "BOTTOM": {"patternId": "arrow_left", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C454\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=N, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=R, rotation=270]\n[LEFT: patternId=W, rotation=90] [TOP: patternId=N, rotation=270] [RIGHT: patternId=arrow_left, rotation=90]\n [FRONT: patternId=J, rotation=0]\n [BOTTOM: patternId=arrow_left, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=R, rotation=270\n- LEFT: patternId=W, rotation=90\n- TOP: patternId=N, rotation=270\n- RIGHT: patternId=arrow_left, rotation=90\n- FRONT: patternId=J, rotation=0\n- BOTTOM: patternId=arrow_left, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C454/initial_net.png", "targetTopFaceImage": "images/C454/target_top_face.png"}, "__sample_id__": "C454"} +{"taskType": "roll_to_target_top_face", "code": "C455", "name": "Goal Roll C455", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "star", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "G", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "diamond", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "star", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "star", "rotation": 180}, "RIGHT": {"patternId": "G", "rotation": 0}, "BACK": {"patternId": "diamond", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "star", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "star", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C455/initial_net.png", "targetTopFaceImage": "../images/C455/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 4, "targetRotationOffset": 270, "levelId": 455, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-455.json"}, "rollSequence": ["E", "S", "N", "N", "W", "S", "N", "W", "S", "S"], "observedPathFaces": [{"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "N", "N", "W", "S", "N", "W", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "star", "rotation": 180}, "RIGHT": {"patternId": "G", "rotation": 0}, "BACK": {"patternId": "diamond", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "star", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C455\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=star, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=diamond, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=G, rotation=0]\n [FRONT: patternId=star, rotation=180]\n [BOTTOM: patternId=star, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=diamond, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=G, rotation=0\n- FRONT: patternId=star, rotation=180\n- BOTTOM: patternId=star, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C455/initial_net.png", "targetTopFaceImage": "images/C455/target_top_face.png"}, "__sample_id__": "C455"} +{"taskType": "roll_to_target_top_face", "code": "C456", "name": "Goal Roll C456", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "B", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "9", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "star", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "Z", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "smile", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "B", "rotation": 270}, "RIGHT": {"patternId": "9", "rotation": 270}, "BACK": {"patternId": "star", "rotation": 90}, "LEFT": {"patternId": "Z", "rotation": 0}, "BOTTOM": {"patternId": "smile", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "Z", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C456/initial_net.png", "targetTopFaceImage": "../images/C456/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 4, "targetRotationOffset": 90, "levelId": 456, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-456.json"}, "rollSequence": ["S", "W", "E", "E", "N", "E", "W", "N", "E", "E"], "observedPathFaces": [{"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "E", "E", "N", "E", "W", "N", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "B", "rotation": 270}, "RIGHT": {"patternId": "9", "rotation": 270}, "BACK": {"patternId": "star", "rotation": 90}, "LEFT": {"patternId": "Z", "rotation": 0}, "BOTTOM": {"patternId": "smile", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C456\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=Z, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=star, rotation=90]\n[LEFT: patternId=Z, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=9, rotation=270]\n [FRONT: patternId=B, rotation=270]\n [BOTTOM: patternId=smile, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=star, rotation=90\n- LEFT: patternId=Z, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=9, rotation=270\n- FRONT: patternId=B, rotation=270\n- BOTTOM: patternId=smile, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C456/initial_net.png", "targetTopFaceImage": "images/C456/target_top_face.png"}, "__sample_id__": "C456"} +{"taskType": "roll_to_target_top_face", "code": "C457", "name": "Goal Roll C457", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "X", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "arrow_up", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "smile", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "7", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "3", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "K", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "X", "rotation": 0}, "FRONT": {"patternId": "arrow_up", "rotation": 270}, "RIGHT": {"patternId": "smile", "rotation": 0}, "BACK": {"patternId": "7", "rotation": 270}, "LEFT": {"patternId": "3", "rotation": 180}, "BOTTOM": {"patternId": "K", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "K", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C457/initial_net.png", "targetTopFaceImage": "../images/C457/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 4, "targetRotationOffset": 180, "levelId": 457, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-457.json"}, "rollSequence": ["W", "S", "S", "W", "S", "S", "S", "E", "S", "W"], "observedPathFaces": [{"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "S", "W", "S", "S", "S", "E", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "X", "rotation": 0}, "FRONT": {"patternId": "arrow_up", "rotation": 270}, "RIGHT": {"patternId": "smile", "rotation": 0}, "BACK": {"patternId": "7", "rotation": 270}, "LEFT": {"patternId": "3", "rotation": 180}, "BOTTOM": {"patternId": "K", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C457\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=K, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=7, rotation=270]\n[LEFT: patternId=3, rotation=180] [TOP: patternId=X, rotation=0] [RIGHT: patternId=smile, rotation=0]\n [FRONT: patternId=arrow_up, rotation=270]\n [BOTTOM: patternId=K, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=7, rotation=270\n- LEFT: patternId=3, rotation=180\n- TOP: patternId=X, rotation=0\n- RIGHT: patternId=smile, rotation=0\n- FRONT: patternId=arrow_up, rotation=270\n- BOTTOM: patternId=K, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C457/initial_net.png", "targetTopFaceImage": "images/C457/target_top_face.png"}, "__sample_id__": "C457"} +{"taskType": "roll_to_target_top_face", "code": "C458", "name": "Goal Roll C458", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "smile", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "F", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "P", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "heart", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "J", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "smile", "rotation": 270}, "FRONT": {"patternId": "F", "rotation": 180}, "RIGHT": {"patternId": "P", "rotation": 180}, "BACK": {"patternId": "heart", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "J", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "F", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C458/initial_net.png", "targetTopFaceImage": "../images/C458/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 458, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-458.json"}, "rollSequence": ["N", "E", "N", "W", "S", "S", "W", "W", "N", "W"], "observedPathFaces": [{"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "N", "W", "S", "S", "W", "W", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "smile", "rotation": 270}, "FRONT": {"patternId": "F", "rotation": 180}, "RIGHT": {"patternId": "P", "rotation": 180}, "BACK": {"patternId": "heart", "rotation": 270}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "J", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C458\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=F, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=heart, rotation=270]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=smile, rotation=270] [RIGHT: patternId=P, rotation=180]\n [FRONT: patternId=F, rotation=180]\n [BOTTOM: patternId=J, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=heart, rotation=270\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=smile, rotation=270\n- RIGHT: patternId=P, rotation=180\n- FRONT: patternId=F, rotation=180\n- BOTTOM: patternId=J, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C458/initial_net.png", "targetTopFaceImage": "images/C458/target_top_face.png"}, "__sample_id__": "C458"} +{"taskType": "roll_to_target_top_face", "code": "C459", "name": "Goal Roll C459", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "smile", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "Z", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "S", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "star", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "L", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "X", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "smile", "rotation": 0}, "FRONT": {"patternId": "Z", "rotation": 270}, "RIGHT": {"patternId": "S", "rotation": 90}, "BACK": {"patternId": "star", "rotation": 180}, "LEFT": {"patternId": "L", "rotation": 270}, "BOTTOM": {"patternId": "X", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "L", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C459/initial_net.png", "targetTopFaceImage": "../images/C459/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 2, "targetRotationOffset": 90, "levelId": 459, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-459.json"}, "rollSequence": ["N", "E", "S", "N", "S", "E", "E", "E", "S", "N"], "observedPathFaces": [{"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "S", "N", "S", "E", "E", "E", "S", "N"]}, "legacy_answer": {"TOP": {"patternId": "smile", "rotation": 0}, "FRONT": {"patternId": "Z", "rotation": 270}, "RIGHT": {"patternId": "S", "rotation": 90}, "BACK": {"patternId": "star", "rotation": 180}, "LEFT": {"patternId": "L", "rotation": 270}, "BOTTOM": {"patternId": "X", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C459\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=L, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=star, rotation=180]\n[LEFT: patternId=L, rotation=270] [TOP: patternId=smile, rotation=0] [RIGHT: patternId=S, rotation=90]\n [FRONT: patternId=Z, rotation=270]\n [BOTTOM: patternId=X, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=star, rotation=180\n- LEFT: patternId=L, rotation=270\n- TOP: patternId=smile, rotation=0\n- RIGHT: patternId=S, rotation=90\n- FRONT: patternId=Z, rotation=270\n- BOTTOM: patternId=X, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C459/initial_net.png", "targetTopFaceImage": "images/C459/target_top_face.png"}, "__sample_id__": "C459"} +{"taskType": "roll_to_target_top_face", "code": "C460", "name": "Goal Roll C460", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "7", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "H", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "B", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "1", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "P", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "D", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "7", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 0}, "RIGHT": {"patternId": "B", "rotation": 270}, "BACK": {"patternId": "1", "rotation": 0}, "LEFT": {"patternId": "P", "rotation": 0}, "BOTTOM": {"patternId": "D", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "D", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C460/initial_net.png", "targetTopFaceImage": "../images/C460/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 2, "targetRotationOffset": 180, "levelId": 460, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-460.json"}, "rollSequence": ["N", "N", "N", "S", "E", "S", "E", "S", "S", "N"], "observedPathFaces": [{"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "N", "S", "E", "S", "E", "S", "S", "N"]}, "legacy_answer": {"TOP": {"patternId": "7", "rotation": 0}, "FRONT": {"patternId": "H", "rotation": 0}, "RIGHT": {"patternId": "B", "rotation": 270}, "BACK": {"patternId": "1", "rotation": 0}, "LEFT": {"patternId": "P", "rotation": 0}, "BOTTOM": {"patternId": "D", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C460\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=D, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=1, rotation=0]\n[LEFT: patternId=P, rotation=0] [TOP: patternId=7, rotation=0] [RIGHT: patternId=B, rotation=270]\n [FRONT: patternId=H, rotation=0]\n [BOTTOM: patternId=D, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=1, rotation=0\n- LEFT: patternId=P, rotation=0\n- TOP: patternId=7, rotation=0\n- RIGHT: patternId=B, rotation=270\n- FRONT: patternId=H, rotation=0\n- BOTTOM: patternId=D, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C460/initial_net.png", "targetTopFaceImage": "images/C460/target_top_face.png"}, "__sample_id__": "C460"} +{"taskType": "roll_to_target_top_face", "code": "C461", "name": "Goal Roll C461", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "plus", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "K", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "A", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "diamond", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "diamond", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "triangle", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "plus", "rotation": 90}, "FRONT": {"patternId": "K", "rotation": 90}, "RIGHT": {"patternId": "A", "rotation": 270}, "BACK": {"patternId": "diamond", "rotation": 180}, "LEFT": {"patternId": "diamond", "rotation": 270}, "BOTTOM": {"patternId": "triangle", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 7, "stepNumber": 8, "patternId": "A", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C461/initial_net.png", "targetTopFaceImage": "../images/C461/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 8, "targetRotationOffset": 90, "levelId": 461, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-461.json"}, "rollSequence": ["E", "E", "N", "E", "N", "N", "E", "E", "N", "S"], "observedPathFaces": [{"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "N", "E", "N", "N", "E", "E", "N", "S"]}, "legacy_answer": {"TOP": {"patternId": "plus", "rotation": 90}, "FRONT": {"patternId": "K", "rotation": 90}, "RIGHT": {"patternId": "A", "rotation": 270}, "BACK": {"patternId": "diamond", "rotation": 180}, "LEFT": {"patternId": "diamond", "rotation": 270}, "BOTTOM": {"patternId": "triangle", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C461\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=A, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=diamond, rotation=180]\n[LEFT: patternId=diamond, rotation=270] [TOP: patternId=plus, rotation=90] [RIGHT: patternId=A, rotation=270]\n [FRONT: patternId=K, rotation=90]\n [BOTTOM: patternId=triangle, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=diamond, rotation=180\n- LEFT: patternId=diamond, rotation=270\n- TOP: patternId=plus, rotation=90\n- RIGHT: patternId=A, rotation=270\n- FRONT: patternId=K, rotation=90\n- BOTTOM: patternId=triangle, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C461/initial_net.png", "targetTopFaceImage": "images/C461/target_top_face.png"}, "__sample_id__": "C461"} +{"taskType": "roll_to_target_top_face", "code": "C462", "name": "Goal Roll C462", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "E", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "1", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_right", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "8", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "5", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "E", "rotation": 0}, "FRONT": {"patternId": "1", "rotation": 90}, "RIGHT": {"patternId": "arrow_right", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 270}, "BOTTOM": {"patternId": "5", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 8, "stepNumber": 9, "patternId": "8", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C462/initial_net.png", "targetTopFaceImage": "../images/C462/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 9, "targetRotationOffset": 180, "levelId": 462, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-462.json"}, "rollSequence": ["W", "S", "N", "S", "W", "S", "E", "S", "W", "N"], "observedPathFaces": [{"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "N", "S", "W", "S", "E", "S", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "E", "rotation": 0}, "FRONT": {"patternId": "1", "rotation": 90}, "RIGHT": {"patternId": "arrow_right", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "8", "rotation": 270}, "BOTTOM": {"patternId": "5", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C462\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=8, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=8, rotation=270] [TOP: patternId=E, rotation=0] [RIGHT: patternId=arrow_right, rotation=270]\n [FRONT: patternId=1, rotation=90]\n [BOTTOM: patternId=5, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=8, rotation=270\n- TOP: patternId=E, rotation=0\n- RIGHT: patternId=arrow_right, rotation=270\n- FRONT: patternId=1, rotation=90\n- BOTTOM: patternId=5, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C462/initial_net.png", "targetTopFaceImage": "images/C462/target_top_face.png"}, "__sample_id__": "C462"} +{"taskType": "roll_to_target_top_face", "code": "C463", "name": "Goal Roll C463", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "D", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "I", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "D", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "T", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "circle", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "J", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "D", "rotation": 0}, "FRONT": {"patternId": "I", "rotation": 270}, "RIGHT": {"patternId": "D", "rotation": 180}, "BACK": {"patternId": "T", "rotation": 90}, "LEFT": {"patternId": "circle", "rotation": 90}, "BOTTOM": {"patternId": "J", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "T", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C463/initial_net.png", "targetTopFaceImage": "../images/C463/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 1, "targetRotationOffset": 180, "levelId": 463, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-463.json"}, "rollSequence": ["S", "S", "N", "W", "S", "S", "E", "S", "E", "S"], "observedPathFaces": [{"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "N", "W", "S", "S", "E", "S", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "D", "rotation": 0}, "FRONT": {"patternId": "I", "rotation": 270}, "RIGHT": {"patternId": "D", "rotation": 180}, "BACK": {"patternId": "T", "rotation": 90}, "LEFT": {"patternId": "circle", "rotation": 90}, "BOTTOM": {"patternId": "J", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C463\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=T, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=T, rotation=90]\n[LEFT: patternId=circle, rotation=90] [TOP: patternId=D, rotation=0] [RIGHT: patternId=D, rotation=180]\n [FRONT: patternId=I, rotation=270]\n [BOTTOM: patternId=J, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=T, rotation=90\n- LEFT: patternId=circle, rotation=90\n- TOP: patternId=D, rotation=0\n- RIGHT: patternId=D, rotation=180\n- FRONT: patternId=I, rotation=270\n- BOTTOM: patternId=J, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C463/initial_net.png", "targetTopFaceImage": "images/C463/target_top_face.png"}, "__sample_id__": "C463"} +{"taskType": "roll_to_target_top_face", "code": "C464", "name": "Goal Roll C464", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "O", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "square", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "T", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "U", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "O", "rotation": 90}, "FRONT": {"patternId": "square", "rotation": 180}, "RIGHT": {"patternId": "T", "rotation": 90}, "BACK": {"patternId": "U", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 8, "stepNumber": 9, "patternId": "square", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C464/initial_net.png", "targetTopFaceImage": "../images/C464/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 9, "targetRotationOffset": 90, "levelId": 464, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-464.json"}, "rollSequence": ["S", "S", "E", "N", "S", "W", "E", "W", "S", "N"], "observedPathFaces": [{"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "E", "N", "S", "W", "E", "W", "S", "N"]}, "legacy_answer": {"TOP": {"patternId": "O", "rotation": 90}, "FRONT": {"patternId": "square", "rotation": 180}, "RIGHT": {"patternId": "T", "rotation": 90}, "BACK": {"patternId": "U", "rotation": 180}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C464\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=square, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=U, rotation=180]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=O, rotation=90] [RIGHT: patternId=T, rotation=90]\n [FRONT: patternId=square, rotation=180]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=U, rotation=180\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=O, rotation=90\n- RIGHT: patternId=T, rotation=90\n- FRONT: patternId=square, rotation=180\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C464/initial_net.png", "targetTopFaceImage": "images/C464/target_top_face.png"}, "__sample_id__": "C464"} +{"taskType": "roll_to_target_top_face", "code": "C465", "name": "Goal Roll C465", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "U", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "G", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "I", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "B", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "M", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "G", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "U", "rotation": 270}, "FRONT": {"patternId": "G", "rotation": 270}, "RIGHT": {"patternId": "I", "rotation": 180}, "BACK": {"patternId": "B", "rotation": 180}, "LEFT": {"patternId": "M", "rotation": 90}, "BOTTOM": {"patternId": "G", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 9, "stepNumber": 10, "patternId": "G", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C465/initial_net.png", "targetTopFaceImage": "../images/C465/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 10, "targetRotationOffset": 90, "levelId": 465, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-465.json"}, "rollSequence": ["N", "W", "S", "S", "E", "S", "N", "E", "E", "S"], "observedPathFaces": [{"patternId": "B", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "S", "S", "E", "S", "N", "E", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "U", "rotation": 270}, "FRONT": {"patternId": "G", "rotation": 270}, "RIGHT": {"patternId": "I", "rotation": 180}, "BACK": {"patternId": "B", "rotation": 180}, "LEFT": {"patternId": "M", "rotation": 90}, "BOTTOM": {"patternId": "G", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C465\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=G, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=B, rotation=180]\n[LEFT: patternId=M, rotation=90] [TOP: patternId=U, rotation=270] [RIGHT: patternId=I, rotation=180]\n [FRONT: patternId=G, rotation=270]\n [BOTTOM: patternId=G, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=B, rotation=180\n- LEFT: patternId=M, rotation=90\n- TOP: patternId=U, rotation=270\n- RIGHT: patternId=I, rotation=180\n- FRONT: patternId=G, rotation=270\n- BOTTOM: patternId=G, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C465/initial_net.png", "targetTopFaceImage": "images/C465/target_top_face.png"}, "__sample_id__": "C465"} +{"taskType": "roll_to_target_top_face", "code": "C466", "name": "Goal Roll C466", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "P", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "8", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "smile", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "smile", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "E", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "E", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "P", "rotation": 270}, "FRONT": {"patternId": "8", "rotation": 0}, "RIGHT": {"patternId": "smile", "rotation": 180}, "BACK": {"patternId": "smile", "rotation": 90}, "LEFT": {"patternId": "E", "rotation": 270}, "BOTTOM": {"patternId": "E", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "E", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C466/initial_net.png", "targetTopFaceImage": "../images/C466/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 2, "targetRotationOffset": 90, "levelId": 466, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-466.json"}, "rollSequence": ["S", "E", "E", "N", "E", "S", "E", "E", "S", "W"], "observedPathFaces": [{"patternId": "8", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "E", "N", "E", "S", "E", "E", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "P", "rotation": 270}, "FRONT": {"patternId": "8", "rotation": 0}, "RIGHT": {"patternId": "smile", "rotation": 180}, "BACK": {"patternId": "smile", "rotation": 90}, "LEFT": {"patternId": "E", "rotation": 270}, "BOTTOM": {"patternId": "E", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C466\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=E, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=smile, rotation=90]\n[LEFT: patternId=E, rotation=270] [TOP: patternId=P, rotation=270] [RIGHT: patternId=smile, rotation=180]\n [FRONT: patternId=8, rotation=0]\n [BOTTOM: patternId=E, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=smile, rotation=90\n- LEFT: patternId=E, rotation=270\n- TOP: patternId=P, rotation=270\n- RIGHT: patternId=smile, rotation=180\n- FRONT: patternId=8, rotation=0\n- BOTTOM: patternId=E, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C466/initial_net.png", "targetTopFaceImage": "images/C466/target_top_face.png"}, "__sample_id__": "C466"} +{"taskType": "roll_to_target_top_face", "code": "C467", "name": "Goal Roll C467", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "2", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "A", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "2", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_left", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "D", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "H", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "2", "rotation": 90}, "FRONT": {"patternId": "A", "rotation": 180}, "RIGHT": {"patternId": "2", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 270}, "LEFT": {"patternId": "D", "rotation": 90}, "BOTTOM": {"patternId": "H", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 9, "stepNumber": 10, "patternId": "D", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C467/initial_net.png", "targetTopFaceImage": "../images/C467/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 10, "targetRotationOffset": 180, "levelId": 467, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-467.json"}, "rollSequence": ["N", "E", "E", "S", "N", "S", "N", "E", "N", "N"], "observedPathFaces": [{"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "E", "S", "N", "S", "N", "E", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "2", "rotation": 90}, "FRONT": {"patternId": "A", "rotation": 180}, "RIGHT": {"patternId": "2", "rotation": 0}, "BACK": {"patternId": "arrow_left", "rotation": 270}, "LEFT": {"patternId": "D", "rotation": 90}, "BOTTOM": {"patternId": "H", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C467\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=D, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_left, rotation=270]\n[LEFT: patternId=D, rotation=90] [TOP: patternId=2, rotation=90] [RIGHT: patternId=2, rotation=0]\n [FRONT: patternId=A, rotation=180]\n [BOTTOM: patternId=H, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_left, rotation=270\n- LEFT: patternId=D, rotation=90\n- TOP: patternId=2, rotation=90\n- RIGHT: patternId=2, rotation=0\n- FRONT: patternId=A, rotation=180\n- BOTTOM: patternId=H, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C467/initial_net.png", "targetTopFaceImage": "images/C467/target_top_face.png"}, "__sample_id__": "C467"} +{"taskType": "roll_to_target_top_face", "code": "C468", "name": "Goal Roll C468", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "circle", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "3", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "2", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "V", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_down", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "4", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "circle", "rotation": 270}, "FRONT": {"patternId": "3", "rotation": 180}, "RIGHT": {"patternId": "2", "rotation": 90}, "BACK": {"patternId": "V", "rotation": 0}, "LEFT": {"patternId": "arrow_down", "rotation": 0}, "BOTTOM": {"patternId": "4", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 8, "stepNumber": 9, "patternId": "3", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C468/initial_net.png", "targetTopFaceImage": "../images/C468/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 9, "targetRotationOffset": 270, "levelId": 468, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-468.json"}, "rollSequence": ["E", "E", "S", "W", "W", "S", "E", "E", "N", "E"], "observedPathFaces": [{"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "V", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "S", "W", "W", "S", "E", "E", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "circle", "rotation": 270}, "FRONT": {"patternId": "3", "rotation": 180}, "RIGHT": {"patternId": "2", "rotation": 90}, "BACK": {"patternId": "V", "rotation": 0}, "LEFT": {"patternId": "arrow_down", "rotation": 0}, "BOTTOM": {"patternId": "4", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C468\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=3, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=V, rotation=0]\n[LEFT: patternId=arrow_down, rotation=0] [TOP: patternId=circle, rotation=270] [RIGHT: patternId=2, rotation=90]\n [FRONT: patternId=3, rotation=180]\n [BOTTOM: patternId=4, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=V, rotation=0\n- LEFT: patternId=arrow_down, rotation=0\n- TOP: patternId=circle, rotation=270\n- RIGHT: patternId=2, rotation=90\n- FRONT: patternId=3, rotation=180\n- BOTTOM: patternId=4, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C468/initial_net.png", "targetTopFaceImage": "images/C468/target_top_face.png"}, "__sample_id__": "C468"} +{"taskType": "roll_to_target_top_face", "code": "C469", "name": "Goal Roll C469", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "smile", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "O", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Z", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "7", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "N", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "G", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "smile", "rotation": 180}, "FRONT": {"patternId": "O", "rotation": 270}, "RIGHT": {"patternId": "Z", "rotation": 90}, "BACK": {"patternId": "7", "rotation": 180}, "LEFT": {"patternId": "N", "rotation": 180}, "BOTTOM": {"patternId": "G", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "Z", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C469/initial_net.png", "targetTopFaceImage": "../images/C469/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 5, "targetRotationOffset": 90, "levelId": 469, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-469.json"}, "rollSequence": ["S", "W", "S", "W", "N", "E", "E", "N", "E", "E"], "observedPathFaces": [{"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "7", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "S", "W", "N", "E", "E", "N", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "smile", "rotation": 180}, "FRONT": {"patternId": "O", "rotation": 270}, "RIGHT": {"patternId": "Z", "rotation": 90}, "BACK": {"patternId": "7", "rotation": 180}, "LEFT": {"patternId": "N", "rotation": 180}, "BOTTOM": {"patternId": "G", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C469\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=Z, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=7, rotation=180]\n[LEFT: patternId=N, rotation=180] [TOP: patternId=smile, rotation=180] [RIGHT: patternId=Z, rotation=90]\n [FRONT: patternId=O, rotation=270]\n [BOTTOM: patternId=G, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=7, rotation=180\n- LEFT: patternId=N, rotation=180\n- TOP: patternId=smile, rotation=180\n- RIGHT: patternId=Z, rotation=90\n- FRONT: patternId=O, rotation=270\n- BOTTOM: patternId=G, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C469/initial_net.png", "targetTopFaceImage": "images/C469/target_top_face.png"}, "__sample_id__": "C469"} +{"taskType": "roll_to_target_top_face", "code": "C470", "name": "Goal Roll C470", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "heart", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "circle", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "A", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "5", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_down", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 270}, "RIGHT": {"patternId": "circle", "rotation": 0}, "BACK": {"patternId": "A", "rotation": 90}, "LEFT": {"patternId": "5", "rotation": 180}, "BOTTOM": {"patternId": "arrow_down", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 9, "stepNumber": 10, "patternId": "5", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C470/initial_net.png", "targetTopFaceImage": "../images/C470/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 10, "targetRotationOffset": 270, "levelId": 470, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-470.json"}, "rollSequence": ["S", "E", "E", "N", "W", "S", "E", "S", "W", "W"], "observedPathFaces": [{"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "E", "N", "W", "S", "E", "S", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "heart", "rotation": 270}, "RIGHT": {"patternId": "circle", "rotation": 0}, "BACK": {"patternId": "A", "rotation": 90}, "LEFT": {"patternId": "5", "rotation": 180}, "BOTTOM": {"patternId": "arrow_down", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C470\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=5, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=A, rotation=90]\n[LEFT: patternId=5, rotation=180] [TOP: patternId=?, rotation=0] [RIGHT: patternId=circle, rotation=0]\n [FRONT: patternId=heart, rotation=270]\n [BOTTOM: patternId=arrow_down, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=A, rotation=90\n- LEFT: patternId=5, rotation=180\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=circle, rotation=0\n- FRONT: patternId=heart, rotation=270\n- BOTTOM: patternId=arrow_down, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C470/initial_net.png", "targetTopFaceImage": "images/C470/target_top_face.png"}, "__sample_id__": "C470"} +{"taskType": "roll_to_target_top_face", "code": "C471", "name": "Goal Roll C471", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "H", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "U", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "triangle", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "W", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "?", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "Q", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "H", "rotation": 180}, "FRONT": {"patternId": "U", "rotation": 180}, "RIGHT": {"patternId": "triangle", "rotation": 90}, "BACK": {"patternId": "W", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "Q", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 7, "stepNumber": 8, "patternId": "H", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C471/initial_net.png", "targetTopFaceImage": "../images/C471/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 8, "targetRotationOffset": 90, "levelId": 471, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-471.json"}, "rollSequence": ["E", "N", "E", "S", "E", "N", "W", "W", "E", "N"], "observedPathFaces": [{"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "U", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "E", "S", "E", "N", "W", "W", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "H", "rotation": 180}, "FRONT": {"patternId": "U", "rotation": 180}, "RIGHT": {"patternId": "triangle", "rotation": 90}, "BACK": {"patternId": "W", "rotation": 0}, "LEFT": {"patternId": "?", "rotation": 0}, "BOTTOM": {"patternId": "Q", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C471\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=H, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=W, rotation=0]\n[LEFT: patternId=?, rotation=0] [TOP: patternId=H, rotation=180] [RIGHT: patternId=triangle, rotation=90]\n [FRONT: patternId=U, rotation=180]\n [BOTTOM: patternId=Q, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=W, rotation=0\n- LEFT: patternId=?, rotation=0\n- TOP: patternId=H, rotation=180\n- RIGHT: patternId=triangle, rotation=90\n- FRONT: patternId=U, rotation=180\n- BOTTOM: patternId=Q, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C471/initial_net.png", "targetTopFaceImage": "images/C471/target_top_face.png"}, "__sample_id__": "C471"} +{"taskType": "roll_to_target_top_face", "code": "C472", "name": "Goal Roll C472", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "5", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "H", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "O", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "M", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "G", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "G", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "5", "rotation": 180}, "FRONT": {"patternId": "H", "rotation": 0}, "RIGHT": {"patternId": "O", "rotation": 90}, "BACK": {"patternId": "M", "rotation": 90}, "LEFT": {"patternId": "G", "rotation": 90}, "BOTTOM": {"patternId": "G", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "H", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C472/initial_net.png", "targetTopFaceImage": "../images/C472/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 1, "targetRotationOffset": 90, "levelId": 472, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-472.json"}, "rollSequence": ["N", "W", "S", "W", "N", "N", "W", "N", "E", "N"], "observedPathFaces": [{"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "S", "W", "N", "N", "W", "N", "E", "N"]}, "legacy_answer": {"TOP": {"patternId": "5", "rotation": 180}, "FRONT": {"patternId": "H", "rotation": 0}, "RIGHT": {"patternId": "O", "rotation": 90}, "BACK": {"patternId": "M", "rotation": 90}, "LEFT": {"patternId": "G", "rotation": 90}, "BOTTOM": {"patternId": "G", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C472\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=H, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=M, rotation=90]\n[LEFT: patternId=G, rotation=90] [TOP: patternId=5, rotation=180] [RIGHT: patternId=O, rotation=90]\n [FRONT: patternId=H, rotation=0]\n [BOTTOM: patternId=G, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=M, rotation=90\n- LEFT: patternId=G, rotation=90\n- TOP: patternId=5, rotation=180\n- RIGHT: patternId=O, rotation=90\n- FRONT: patternId=H, rotation=0\n- BOTTOM: patternId=G, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C472/initial_net.png", "targetTopFaceImage": "images/C472/target_top_face.png"}, "__sample_id__": "C472"} +{"taskType": "roll_to_target_top_face", "code": "C473", "name": "Goal Roll C473", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "I", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "X", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Y", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "heart", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "triangle", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "I", "rotation": 180}, "FRONT": {"patternId": "X", "rotation": 270}, "RIGHT": {"patternId": "Y", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "heart", "rotation": 90}, "BOTTOM": {"patternId": "triangle", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 8, "stepNumber": 9, "patternId": "heart", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C473/initial_net.png", "targetTopFaceImage": "../images/C473/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 9, "targetRotationOffset": 180, "levelId": 473, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-473.json"}, "rollSequence": ["E", "S", "W", "E", "S", "N", "S", "E", "E", "E"], "observedPathFaces": [{"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "W", "E", "S", "N", "S", "E", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "I", "rotation": 180}, "FRONT": {"patternId": "X", "rotation": 270}, "RIGHT": {"patternId": "Y", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "heart", "rotation": 90}, "BOTTOM": {"patternId": "triangle", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C473\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=heart, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=heart, rotation=90] [TOP: patternId=I, rotation=180] [RIGHT: patternId=Y, rotation=0]\n [FRONT: patternId=X, rotation=270]\n [BOTTOM: patternId=triangle, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=heart, rotation=90\n- TOP: patternId=I, rotation=180\n- RIGHT: patternId=Y, rotation=0\n- FRONT: patternId=X, rotation=270\n- BOTTOM: patternId=triangle, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C473/initial_net.png", "targetTopFaceImage": "images/C473/target_top_face.png"}, "__sample_id__": "C473"} +{"taskType": "roll_to_target_top_face", "code": "C474", "name": "Goal Roll C474", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "arrow_right", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "L", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "plus", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "N", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "triangle", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "arrow_right", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "L", "rotation": 180}, "BACK": {"patternId": "plus", "rotation": 180}, "LEFT": {"patternId": "N", "rotation": 180}, "BOTTOM": {"patternId": "triangle", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "triangle", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C474/initial_net.png", "targetTopFaceImage": "../images/C474/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 5, "targetRotationOffset": 180, "levelId": 474, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-474.json"}, "rollSequence": ["N", "W", "E", "E", "N", "N", "W", "N", "S", "N"], "observedPathFaces": [{"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "E", "E", "N", "N", "W", "N", "S", "N"]}, "legacy_answer": {"TOP": {"patternId": "arrow_right", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "L", "rotation": 180}, "BACK": {"patternId": "plus", "rotation": 180}, "LEFT": {"patternId": "N", "rotation": 180}, "BOTTOM": {"patternId": "triangle", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C474\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=triangle, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=plus, rotation=180]\n[LEFT: patternId=N, rotation=180] [TOP: patternId=arrow_right, rotation=270] [RIGHT: patternId=L, rotation=180]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=triangle, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=plus, rotation=180\n- LEFT: patternId=N, rotation=180\n- TOP: patternId=arrow_right, rotation=270\n- RIGHT: patternId=L, rotation=180\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=triangle, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C474/initial_net.png", "targetTopFaceImage": "images/C474/target_top_face.png"}, "__sample_id__": "C474"} +{"taskType": "roll_to_target_top_face", "code": "C475", "name": "Goal Roll C475", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "C", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "9", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_right", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "R", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "1", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "triangle", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "C", "rotation": 180}, "FRONT": {"patternId": "9", "rotation": 270}, "RIGHT": {"patternId": "arrow_right", "rotation": 180}, "BACK": {"patternId": "R", "rotation": 180}, "LEFT": {"patternId": "1", "rotation": 90}, "BOTTOM": {"patternId": "triangle", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 6, "stepNumber": 7, "patternId": "triangle", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C475/initial_net.png", "targetTopFaceImage": "../images/C475/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 7, "targetRotationOffset": 180, "levelId": 475, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-475.json"}, "rollSequence": ["S", "S", "W", "N", "N", "N", "E", "N", "N", "E"], "observedPathFaces": [{"patternId": "9", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "S", "W", "N", "N", "N", "E", "N", "N", "E"]}, "legacy_answer": {"TOP": {"patternId": "C", "rotation": 180}, "FRONT": {"patternId": "9", "rotation": 270}, "RIGHT": {"patternId": "arrow_right", "rotation": 180}, "BACK": {"patternId": "R", "rotation": 180}, "LEFT": {"patternId": "1", "rotation": 90}, "BOTTOM": {"patternId": "triangle", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C475\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=triangle, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=R, rotation=180]\n[LEFT: patternId=1, rotation=90] [TOP: patternId=C, rotation=180] [RIGHT: patternId=arrow_right, rotation=180]\n [FRONT: patternId=9, rotation=270]\n [BOTTOM: patternId=triangle, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=R, rotation=180\n- LEFT: patternId=1, rotation=90\n- TOP: patternId=C, rotation=180\n- RIGHT: patternId=arrow_right, rotation=180\n- FRONT: patternId=9, rotation=270\n- BOTTOM: patternId=triangle, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C475/initial_net.png", "targetTopFaceImage": "images/C475/target_top_face.png"}, "__sample_id__": "C475"} +{"taskType": "roll_to_target_top_face", "code": "C476", "name": "Goal Roll C476", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "5", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "F", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Q", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "circle", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "I", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "9", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "5", "rotation": 90}, "FRONT": {"patternId": "F", "rotation": 90}, "RIGHT": {"patternId": "Q", "rotation": 270}, "BACK": {"patternId": "circle", "rotation": 180}, "LEFT": {"patternId": "I", "rotation": 270}, "BOTTOM": {"patternId": "9", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 8, "stepNumber": 9, "patternId": "Q", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C476/initial_net.png", "targetTopFaceImage": "../images/C476/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 9, "targetRotationOffset": 270, "levelId": 476, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-476.json"}, "rollSequence": ["W", "W", "S", "W", "S", "N", "N", "W", "N", "N"], "observedPathFaces": [{"patternId": "I", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "I", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "S", "W", "S", "N", "N", "W", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "5", "rotation": 90}, "FRONT": {"patternId": "F", "rotation": 90}, "RIGHT": {"patternId": "Q", "rotation": 270}, "BACK": {"patternId": "circle", "rotation": 180}, "LEFT": {"patternId": "I", "rotation": 270}, "BOTTOM": {"patternId": "9", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C476\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=Q, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=circle, rotation=180]\n[LEFT: patternId=I, rotation=270] [TOP: patternId=5, rotation=90] [RIGHT: patternId=Q, rotation=270]\n [FRONT: patternId=F, rotation=90]\n [BOTTOM: patternId=9, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=circle, rotation=180\n- LEFT: patternId=I, rotation=270\n- TOP: patternId=5, rotation=90\n- RIGHT: patternId=Q, rotation=270\n- FRONT: patternId=F, rotation=90\n- BOTTOM: patternId=9, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C476/initial_net.png", "targetTopFaceImage": "images/C476/target_top_face.png"}, "__sample_id__": "C476"} +{"taskType": "roll_to_target_top_face", "code": "C477", "name": "Goal Roll C477", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "C", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "O", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "C", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "D", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "6", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "C", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "O", "rotation": 270}, "BACK": {"patternId": "C", "rotation": 90}, "LEFT": {"patternId": "D", "rotation": 270}, "BOTTOM": {"patternId": "6", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 6, "stepNumber": 7, "patternId": "O", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C477/initial_net.png", "targetTopFaceImage": "../images/C477/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 7, "targetRotationOffset": 180, "levelId": 477, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-477.json"}, "rollSequence": ["W", "W", "N", "W", "E", "N", "E", "E", "E", "W"], "observedPathFaces": [{"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "N", "W", "E", "N", "E", "E", "E", "W"]}, "legacy_answer": {"TOP": {"patternId": "C", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "O", "rotation": 270}, "BACK": {"patternId": "C", "rotation": 90}, "LEFT": {"patternId": "D", "rotation": 270}, "BOTTOM": {"patternId": "6", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C477\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=O, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=C, rotation=90]\n[LEFT: patternId=D, rotation=270] [TOP: patternId=C, rotation=0] [RIGHT: patternId=O, rotation=270]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=6, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=C, rotation=90\n- LEFT: patternId=D, rotation=270\n- TOP: patternId=C, rotation=0\n- RIGHT: patternId=O, rotation=270\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=6, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C477/initial_net.png", "targetTopFaceImage": "images/C477/target_top_face.png"}, "__sample_id__": "C477"} +{"taskType": "roll_to_target_top_face", "code": "C478", "name": "Goal Roll C478", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "triangle", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "C", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "O", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "Y", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "D", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "triangle", "rotation": 0}, "FRONT": {"patternId": "C", "rotation": 0}, "RIGHT": {"patternId": "O", "rotation": 270}, "BACK": {"patternId": "Y", "rotation": 180}, "LEFT": {"patternId": "D", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "O", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C478/initial_net.png", "targetTopFaceImage": "../images/C478/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 3, "targetRotationOffset": 180, "levelId": 478, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-478.json"}, "rollSequence": ["E", "E", "E", "S", "S", "W", "W", "S", "E", "W"], "observedPathFaces": [{"patternId": "O", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "O", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "E", "S", "S", "W", "W", "S", "E", "W"]}, "legacy_answer": {"TOP": {"patternId": "triangle", "rotation": 0}, "FRONT": {"patternId": "C", "rotation": 0}, "RIGHT": {"patternId": "O", "rotation": 270}, "BACK": {"patternId": "Y", "rotation": 180}, "LEFT": {"patternId": "D", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C478\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=O, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=Y, rotation=180]\n[LEFT: patternId=D, rotation=90] [TOP: patternId=triangle, rotation=0] [RIGHT: patternId=O, rotation=270]\n [FRONT: patternId=C, rotation=0]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Y, rotation=180\n- LEFT: patternId=D, rotation=90\n- TOP: patternId=triangle, rotation=0\n- RIGHT: patternId=O, rotation=270\n- FRONT: patternId=C, rotation=0\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C478/initial_net.png", "targetTopFaceImage": "images/C478/target_top_face.png"}, "__sample_id__": "C478"} +{"taskType": "roll_to_target_top_face", "code": "C479", "name": "Goal Roll C479", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "Z", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "Y", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "E", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "G", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "E", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "Z", "rotation": 0}, "FRONT": {"patternId": "Y", "rotation": 90}, "RIGHT": {"patternId": "E", "rotation": 0}, "BACK": {"patternId": "G", "rotation": 180}, "LEFT": {"patternId": "E", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 1, "stepNumber": 2, "patternId": "E", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C479/initial_net.png", "targetTopFaceImage": "../images/C479/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 2, "targetRotationOffset": 180, "levelId": 479, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-479.json"}, "rollSequence": ["S", "W", "E", "S", "N", "W", "W", "W", "S", "W"], "observedPathFaces": [{"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "E", "S", "N", "W", "W", "W", "S", "W"]}, "legacy_answer": {"TOP": {"patternId": "Z", "rotation": 0}, "FRONT": {"patternId": "Y", "rotation": 90}, "RIGHT": {"patternId": "E", "rotation": 0}, "BACK": {"patternId": "G", "rotation": 180}, "LEFT": {"patternId": "E", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C479\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=E, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=G, rotation=180]\n[LEFT: patternId=E, rotation=0] [TOP: patternId=Z, rotation=0] [RIGHT: patternId=E, rotation=0]\n [FRONT: patternId=Y, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=G, rotation=180\n- LEFT: patternId=E, rotation=0\n- TOP: patternId=Z, rotation=0\n- RIGHT: patternId=E, rotation=0\n- FRONT: patternId=Y, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C479/initial_net.png", "targetTopFaceImage": "images/C479/target_top_face.png"}, "__sample_id__": "C479"} +{"taskType": "roll_to_target_top_face", "code": "C480", "name": "Goal Roll C480", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "Q", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "E", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "diamond", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "N", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "F", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "8", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "Q", "rotation": 90}, "FRONT": {"patternId": "E", "rotation": 180}, "RIGHT": {"patternId": "diamond", "rotation": 180}, "BACK": {"patternId": "N", "rotation": 90}, "LEFT": {"patternId": "F", "rotation": 270}, "BOTTOM": {"patternId": "8", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "Q", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C480/initial_net.png", "targetTopFaceImage": "../images/C480/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 6, "targetRotationOffset": 180, "levelId": 480, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-480.json"}, "rollSequence": ["W", "N", "W", "E", "S", "E", "W", "N", "N", "N"], "observedPathFaces": [{"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "8", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "N", "W", "E", "S", "E", "W", "N", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "Q", "rotation": 90}, "FRONT": {"patternId": "E", "rotation": 180}, "RIGHT": {"patternId": "diamond", "rotation": 180}, "BACK": {"patternId": "N", "rotation": 90}, "LEFT": {"patternId": "F", "rotation": 270}, "BOTTOM": {"patternId": "8", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C480\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=Q, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=N, rotation=90]\n[LEFT: patternId=F, rotation=270] [TOP: patternId=Q, rotation=90] [RIGHT: patternId=diamond, rotation=180]\n [FRONT: patternId=E, rotation=180]\n [BOTTOM: patternId=8, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=N, rotation=90\n- LEFT: patternId=F, rotation=270\n- TOP: patternId=Q, rotation=90\n- RIGHT: patternId=diamond, rotation=180\n- FRONT: patternId=E, rotation=180\n- BOTTOM: patternId=8, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C480/initial_net.png", "targetTopFaceImage": "images/C480/target_top_face.png"}, "__sample_id__": "C480"} +{"taskType": "roll_to_target_top_face", "code": "C481", "name": "Goal Roll C481", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "6", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "square", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "M", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "S", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "K", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "6", "rotation": 180}, "FRONT": {"patternId": "square", "rotation": 270}, "RIGHT": {"patternId": "M", "rotation": 90}, "BACK": {"patternId": "S", "rotation": 90}, "LEFT": {"patternId": "K", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "square", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C481/initial_net.png", "targetTopFaceImage": "../images/C481/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 6, "targetRotationOffset": 270, "levelId": 481, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-481.json"}, "rollSequence": ["N", "W", "W", "N", "E", "N", "W", "N", "E", "E"], "observedPathFaces": [{"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "W", "N", "E", "N", "W", "N", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "6", "rotation": 180}, "FRONT": {"patternId": "square", "rotation": 270}, "RIGHT": {"patternId": "M", "rotation": 90}, "BACK": {"patternId": "S", "rotation": 90}, "LEFT": {"patternId": "K", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C481\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=square, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=S, rotation=90]\n[LEFT: patternId=K, rotation=180] [TOP: patternId=6, rotation=180] [RIGHT: patternId=M, rotation=90]\n [FRONT: patternId=square, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=S, rotation=90\n- LEFT: patternId=K, rotation=180\n- TOP: patternId=6, rotation=180\n- RIGHT: patternId=M, rotation=90\n- FRONT: patternId=square, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C481/initial_net.png", "targetTopFaceImage": "images/C481/target_top_face.png"}, "__sample_id__": "C481"} +{"taskType": "roll_to_target_top_face", "code": "C482", "name": "Goal Roll C482", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "L", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "D", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "J", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "diamond", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "1", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "L", "rotation": 180}, "FRONT": {"patternId": "D", "rotation": 270}, "RIGHT": {"patternId": "J", "rotation": 180}, "BACK": {"patternId": "diamond", "rotation": 270}, "LEFT": {"patternId": "1", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "diamond", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C482/initial_net.png", "targetTopFaceImage": "../images/C482/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 3, "targetRotationOffset": 90, "levelId": 482, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-482.json"}, "rollSequence": ["S", "E", "W", "W", "E", "S", "E", "S", "S", "S"], "observedPathFaces": [{"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "L", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "W", "W", "E", "S", "E", "S", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "L", "rotation": 180}, "FRONT": {"patternId": "D", "rotation": 270}, "RIGHT": {"patternId": "J", "rotation": 180}, "BACK": {"patternId": "diamond", "rotation": 270}, "LEFT": {"patternId": "1", "rotation": 270}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C482\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=diamond, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=diamond, rotation=270]\n[LEFT: patternId=1, rotation=270] [TOP: patternId=L, rotation=180] [RIGHT: patternId=J, rotation=180]\n [FRONT: patternId=D, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=diamond, rotation=270\n- LEFT: patternId=1, rotation=270\n- TOP: patternId=L, rotation=180\n- RIGHT: patternId=J, rotation=180\n- FRONT: patternId=D, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C482/initial_net.png", "targetTopFaceImage": "images/C482/target_top_face.png"}, "__sample_id__": "C482"} +{"taskType": "roll_to_target_top_face", "code": "C483", "name": "Goal Roll C483", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "star", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "F", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "9", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "P", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_down", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "star", "rotation": 0}, "FRONT": {"patternId": "F", "rotation": 270}, "RIGHT": {"patternId": "9", "rotation": 0}, "BACK": {"patternId": "P", "rotation": 180}, "LEFT": {"patternId": "arrow_down", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "F", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C483/initial_net.png", "targetTopFaceImage": "../images/C483/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 5, "targetRotationOffset": 270, "levelId": 483, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-483.json"}, "rollSequence": ["N", "W", "N", "N", "E", "E", "S", "E", "S", "S"], "observedPathFaces": [{"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_down", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "9", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "N", "N", "E", "E", "S", "E", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "star", "rotation": 0}, "FRONT": {"patternId": "F", "rotation": 270}, "RIGHT": {"patternId": "9", "rotation": 0}, "BACK": {"patternId": "P", "rotation": 180}, "LEFT": {"patternId": "arrow_down", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C483\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=F, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=P, rotation=180]\n[LEFT: patternId=arrow_down, rotation=180] [TOP: patternId=star, rotation=0] [RIGHT: patternId=9, rotation=0]\n [FRONT: patternId=F, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=P, rotation=180\n- LEFT: patternId=arrow_down, rotation=180\n- TOP: patternId=star, rotation=0\n- RIGHT: patternId=9, rotation=0\n- FRONT: patternId=F, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C483/initial_net.png", "targetTopFaceImage": "images/C483/target_top_face.png"}, "__sample_id__": "C483"} +{"taskType": "roll_to_target_top_face", "code": "C484", "name": "Goal Roll C484", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "arrow_up", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "Q", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "diamond", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "R", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "R", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "square", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "arrow_up", "rotation": 270}, "FRONT": {"patternId": "Q", "rotation": 270}, "RIGHT": {"patternId": "diamond", "rotation": 90}, "BACK": {"patternId": "R", "rotation": 180}, "LEFT": {"patternId": "R", "rotation": 180}, "BOTTOM": {"patternId": "square", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "Q", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C484/initial_net.png", "targetTopFaceImage": "../images/C484/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 5, "targetRotationOffset": 270, "levelId": 484, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-484.json"}, "rollSequence": ["N", "N", "N", "E", "E", "N", "E", "W", "N", "S"], "observedPathFaces": [{"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "N", "E", "E", "N", "E", "W", "N", "S"]}, "legacy_answer": {"TOP": {"patternId": "arrow_up", "rotation": 270}, "FRONT": {"patternId": "Q", "rotation": 270}, "RIGHT": {"patternId": "diamond", "rotation": 90}, "BACK": {"patternId": "R", "rotation": 180}, "LEFT": {"patternId": "R", "rotation": 180}, "BOTTOM": {"patternId": "square", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C484\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=Q, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=R, rotation=180]\n[LEFT: patternId=R, rotation=180] [TOP: patternId=arrow_up, rotation=270] [RIGHT: patternId=diamond, rotation=90]\n [FRONT: patternId=Q, rotation=270]\n [BOTTOM: patternId=square, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=R, rotation=180\n- LEFT: patternId=R, rotation=180\n- TOP: patternId=arrow_up, rotation=270\n- RIGHT: patternId=diamond, rotation=90\n- FRONT: patternId=Q, rotation=270\n- BOTTOM: patternId=square, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C484/initial_net.png", "targetTopFaceImage": "images/C484/target_top_face.png"}, "__sample_id__": "C484"} +{"taskType": "roll_to_target_top_face", "code": "C485", "name": "Goal Roll C485", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "B", "rotation": 180}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "P", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "D", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "K", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "heart", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_left", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "B", "rotation": 180}, "FRONT": {"patternId": "P", "rotation": 90}, "RIGHT": {"patternId": "D", "rotation": 90}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "heart", "rotation": 0}, "BOTTOM": {"patternId": "arrow_left", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 9, "stepNumber": 10, "patternId": "D", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C485/initial_net.png", "targetTopFaceImage": "../images/C485/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 10, "targetRotationOffset": 90, "levelId": 485, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-485.json"}, "rollSequence": ["S", "E", "E", "S", "W", "S", "W", "N", "N", "N"], "observedPathFaces": [{"patternId": "P", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "P", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "E", "S", "W", "S", "W", "N", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "B", "rotation": 180}, "FRONT": {"patternId": "P", "rotation": 90}, "RIGHT": {"patternId": "D", "rotation": 90}, "BACK": {"patternId": "K", "rotation": 270}, "LEFT": {"patternId": "heart", "rotation": 0}, "BOTTOM": {"patternId": "arrow_left", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C485\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=D, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=K, rotation=270]\n[LEFT: patternId=heart, rotation=0] [TOP: patternId=B, rotation=180] [RIGHT: patternId=D, rotation=90]\n [FRONT: patternId=P, rotation=90]\n [BOTTOM: patternId=arrow_left, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=K, rotation=270\n- LEFT: patternId=heart, rotation=0\n- TOP: patternId=B, rotation=180\n- RIGHT: patternId=D, rotation=90\n- FRONT: patternId=P, rotation=90\n- BOTTOM: patternId=arrow_left, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C485/initial_net.png", "targetTopFaceImage": "images/C485/target_top_face.png"}, "__sample_id__": "C485"} +{"taskType": "roll_to_target_top_face", "code": "C486", "name": "Goal Roll C486", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "circle", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "H", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "W", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "2", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "K", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_left", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "circle", "rotation": 270}, "FRONT": {"patternId": "H", "rotation": 270}, "RIGHT": {"patternId": "W", "rotation": 270}, "BACK": {"patternId": "2", "rotation": 270}, "LEFT": {"patternId": "K", "rotation": 270}, "BOTTOM": {"patternId": "arrow_left", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 5, "stepNumber": 6, "patternId": "K", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C486/initial_net.png", "targetTopFaceImage": "../images/C486/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 6, "targetRotationOffset": 90, "levelId": 486, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-486.json"}, "rollSequence": ["S", "W", "S", "E", "W", "S", "W", "N", "W", "W"], "observedPathFaces": [{"patternId": "H", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "H", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "W", "S", "E", "W", "S", "W", "N", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "circle", "rotation": 270}, "FRONT": {"patternId": "H", "rotation": 270}, "RIGHT": {"patternId": "W", "rotation": 270}, "BACK": {"patternId": "2", "rotation": 270}, "LEFT": {"patternId": "K", "rotation": 270}, "BOTTOM": {"patternId": "arrow_left", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C486\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=K, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=2, rotation=270]\n[LEFT: patternId=K, rotation=270] [TOP: patternId=circle, rotation=270] [RIGHT: patternId=W, rotation=270]\n [FRONT: patternId=H, rotation=270]\n [BOTTOM: patternId=arrow_left, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=2, rotation=270\n- LEFT: patternId=K, rotation=270\n- TOP: patternId=circle, rotation=270\n- RIGHT: patternId=W, rotation=270\n- FRONT: patternId=H, rotation=270\n- BOTTOM: patternId=arrow_left, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C486/initial_net.png", "targetTopFaceImage": "images/C486/target_top_face.png"}, "__sample_id__": "C486"} +{"taskType": "roll_to_target_top_face", "code": "C487", "name": "Goal Roll C487", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "arrow_right", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "E", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "D", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "arrow_up", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "D", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "arrow_right", "rotation": 90}, "FRONT": {"patternId": "E", "rotation": 90}, "RIGHT": {"patternId": "D", "rotation": 180}, "BACK": {"patternId": "arrow_up", "rotation": 0}, "LEFT": {"patternId": "D", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 7, "stepNumber": 8, "patternId": "arrow_up", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C487/initial_net.png", "targetTopFaceImage": "../images/C487/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 8, "targetRotationOffset": 180, "levelId": 487, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-487.json"}, "rollSequence": ["S", "E", "S", "E", "N", "N", "N", "S", "N", "N"], "observedPathFaces": [{"patternId": "E", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "D", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "S", "E", "N", "N", "N", "S", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "arrow_right", "rotation": 90}, "FRONT": {"patternId": "E", "rotation": 90}, "RIGHT": {"patternId": "D", "rotation": 180}, "BACK": {"patternId": "arrow_up", "rotation": 0}, "LEFT": {"patternId": "D", "rotation": 0}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C487\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=arrow_up, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=arrow_up, rotation=0]\n[LEFT: patternId=D, rotation=0] [TOP: patternId=arrow_right, rotation=90] [RIGHT: patternId=D, rotation=180]\n [FRONT: patternId=E, rotation=90]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=arrow_up, rotation=0\n- LEFT: patternId=D, rotation=0\n- TOP: patternId=arrow_right, rotation=90\n- RIGHT: patternId=D, rotation=180\n- FRONT: patternId=E, rotation=90\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C487/initial_net.png", "targetTopFaceImage": "images/C487/target_top_face.png"}, "__sample_id__": "C487"} +{"taskType": "roll_to_target_top_face", "code": "C488", "name": "Goal Roll C488", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "Y", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "M", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "M", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "Q", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "X", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "Y", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "M", "rotation": 180}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "Q", "rotation": 90}, "BOTTOM": {"patternId": "X", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 6, "stepNumber": 7, "patternId": "M", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C488/initial_net.png", "targetTopFaceImage": "../images/C488/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 7, "targetRotationOffset": 180, "levelId": 488, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-488.json"}, "rollSequence": ["N", "W", "S", "S", "S", "E", "S", "E", "N", "N"], "observedPathFaces": [{"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Q", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Y", "rotation": 0, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "S", "S", "S", "E", "S", "E", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "Y", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "M", "rotation": 180}, "BACK": {"patternId": "M", "rotation": 0}, "LEFT": {"patternId": "Q", "rotation": 90}, "BOTTOM": {"patternId": "X", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C488\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=M, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=M, rotation=0]\n[LEFT: patternId=Q, rotation=90] [TOP: patternId=Y, rotation=0] [RIGHT: patternId=M, rotation=180]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=X, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=M, rotation=0\n- LEFT: patternId=Q, rotation=90\n- TOP: patternId=Y, rotation=0\n- RIGHT: patternId=M, rotation=180\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=X, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C488/initial_net.png", "targetTopFaceImage": "images/C488/target_top_face.png"}, "__sample_id__": "C488"} +{"taskType": "roll_to_target_top_face", "code": "C489", "name": "Goal Roll C489", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "smile", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "M", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "diamond", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "X", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "6", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "smile", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "M", "rotation": 90}, "BACK": {"patternId": "diamond", "rotation": 0}, "LEFT": {"patternId": "X", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "X", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C489/initial_net.png", "targetTopFaceImage": "../images/C489/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 3, "targetRotationOffset": 180, "levelId": 489, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-489.json"}, "rollSequence": ["N", "N", "E", "S", "E", "N", "W", "W", "S", "S"], "observedPathFaces": [{"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "diamond", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "M", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "E", "S", "E", "N", "W", "W", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "smile", "rotation": 0}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "M", "rotation": 90}, "BACK": {"patternId": "diamond", "rotation": 0}, "LEFT": {"patternId": "X", "rotation": 0}, "BOTTOM": {"patternId": "6", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C489\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=X, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=diamond, rotation=0]\n[LEFT: patternId=X, rotation=0] [TOP: patternId=smile, rotation=0] [RIGHT: patternId=M, rotation=90]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=6, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=diamond, rotation=0\n- LEFT: patternId=X, rotation=0\n- TOP: patternId=smile, rotation=0\n- RIGHT: patternId=M, rotation=90\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=6, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C489/initial_net.png", "targetTopFaceImage": "images/C489/target_top_face.png"}, "__sample_id__": "C489"} +{"taskType": "roll_to_target_top_face", "code": "C490", "name": "Goal Roll C490", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "2", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "E", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "S", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "Z", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "N", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "5", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "2", "rotation": 270}, "FRONT": {"patternId": "E", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 90}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "N", "rotation": 180}, "BOTTOM": {"patternId": "5", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 3, "stepNumber": 4, "patternId": "2", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C490/initial_net.png", "targetTopFaceImage": "../images/C490/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 4, "targetRotationOffset": 180, "levelId": 490, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-490.json"}, "rollSequence": ["N", "E", "W", "S", "W", "N", "W", "N", "W", "S"], "observedPathFaces": [{"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "N", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "E", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "W", "S", "W", "N", "W", "N", "W", "S"]}, "legacy_answer": {"TOP": {"patternId": "2", "rotation": 270}, "FRONT": {"patternId": "E", "rotation": 0}, "RIGHT": {"patternId": "S", "rotation": 90}, "BACK": {"patternId": "Z", "rotation": 90}, "LEFT": {"patternId": "N", "rotation": 180}, "BOTTOM": {"patternId": "5", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C490\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=2, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=Z, rotation=90]\n[LEFT: patternId=N, rotation=180] [TOP: patternId=2, rotation=270] [RIGHT: patternId=S, rotation=90]\n [FRONT: patternId=E, rotation=0]\n [BOTTOM: patternId=5, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=Z, rotation=90\n- LEFT: patternId=N, rotation=180\n- TOP: patternId=2, rotation=270\n- RIGHT: patternId=S, rotation=90\n- FRONT: patternId=E, rotation=0\n- BOTTOM: patternId=5, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C490/initial_net.png", "targetTopFaceImage": "images/C490/target_top_face.png"}, "__sample_id__": "C490"} +{"taskType": "roll_to_target_top_face", "code": "C491", "name": "Goal Roll C491", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "4", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "X", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "B", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "Z", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_left", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "4", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "X", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 0}, "LEFT": {"patternId": "Z", "rotation": 270}, "BOTTOM": {"patternId": "arrow_left", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 2, "stepNumber": 3, "patternId": "Z", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C491/initial_net.png", "targetTopFaceImage": "../images/C491/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 3, "targetRotationOffset": 270, "levelId": 491, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-491.json"}, "rollSequence": ["E", "E", "W", "W", "N", "W", "N", "E", "E", "S"], "observedPathFaces": [{"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "W", "W", "N", "W", "N", "E", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "4", "rotation": 270}, "FRONT": {"patternId": "?", "rotation": 0}, "RIGHT": {"patternId": "X", "rotation": 0}, "BACK": {"patternId": "B", "rotation": 0}, "LEFT": {"patternId": "Z", "rotation": 270}, "BOTTOM": {"patternId": "arrow_left", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C491\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=Z, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=B, rotation=0]\n[LEFT: patternId=Z, rotation=270] [TOP: patternId=4, rotation=270] [RIGHT: patternId=X, rotation=0]\n [FRONT: patternId=?, rotation=0]\n [BOTTOM: patternId=arrow_left, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=B, rotation=0\n- LEFT: patternId=Z, rotation=270\n- TOP: patternId=4, rotation=270\n- RIGHT: patternId=X, rotation=0\n- FRONT: patternId=?, rotation=0\n- BOTTOM: patternId=arrow_left, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C491/initial_net.png", "targetTopFaceImage": "images/C491/target_top_face.png"}, "__sample_id__": "C491"} +{"taskType": "roll_to_target_top_face", "code": "C492", "name": "Goal Roll C492", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "K", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "star", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "X", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "F", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "F", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "K", "rotation": 270}, "FRONT": {"patternId": "star", "rotation": 270}, "RIGHT": {"patternId": "X", "rotation": 270}, "BACK": {"patternId": "F", "rotation": 0}, "LEFT": {"patternId": "F", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 8, "stepNumber": 9, "patternId": "X", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C492/initial_net.png", "targetTopFaceImage": "../images/C492/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 9, "targetRotationOffset": 270, "levelId": 492, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-492.json"}, "rollSequence": ["N", "W", "N", "N", "E", "E", "S", "E", "N", "N"], "observedPathFaces": [{"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "W", "N", "N", "E", "E", "S", "E", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "K", "rotation": 270}, "FRONT": {"patternId": "star", "rotation": 270}, "RIGHT": {"patternId": "X", "rotation": 270}, "BACK": {"patternId": "F", "rotation": 0}, "LEFT": {"patternId": "F", "rotation": 180}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C492\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=X, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=F, rotation=0]\n[LEFT: patternId=F, rotation=180] [TOP: patternId=K, rotation=270] [RIGHT: patternId=X, rotation=270]\n [FRONT: patternId=star, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=F, rotation=0\n- LEFT: patternId=F, rotation=180\n- TOP: patternId=K, rotation=270\n- RIGHT: patternId=X, rotation=270\n- FRONT: patternId=star, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C492/initial_net.png", "targetTopFaceImage": "images/C492/target_top_face.png"}, "__sample_id__": "C492"} +{"taskType": "roll_to_target_top_face", "code": "C493", "name": "Goal Roll C493", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "5", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "B", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_up", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "W", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "star", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "?", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "5", "rotation": 90}, "FRONT": {"patternId": "B", "rotation": 270}, "RIGHT": {"patternId": "arrow_up", "rotation": 0}, "BACK": {"patternId": "W", "rotation": 180}, "LEFT": {"patternId": "star", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 8, "stepNumber": 9, "patternId": "W", "rotation": 90}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C493/initial_net.png", "targetTopFaceImage": "../images/C493/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 9, "targetRotationOffset": 270, "levelId": 493, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-493.json"}, "rollSequence": ["E", "N", "N", "N", "S", "E", "S", "W", "W", "N"], "observedPathFaces": [{"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "star", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "B", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "5", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "N", "N", "N", "S", "E", "S", "W", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "5", "rotation": 90}, "FRONT": {"patternId": "B", "rotation": 270}, "RIGHT": {"patternId": "arrow_up", "rotation": 0}, "BACK": {"patternId": "W", "rotation": 180}, "LEFT": {"patternId": "star", "rotation": 90}, "BOTTOM": {"patternId": "?", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C493\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=W, rotation=90\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=W, rotation=180]\n[LEFT: patternId=star, rotation=90] [TOP: patternId=5, rotation=90] [RIGHT: patternId=arrow_up, rotation=0]\n [FRONT: patternId=B, rotation=270]\n [BOTTOM: patternId=?, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=W, rotation=180\n- LEFT: patternId=star, rotation=90\n- TOP: patternId=5, rotation=90\n- RIGHT: patternId=arrow_up, rotation=0\n- FRONT: patternId=B, rotation=270\n- BOTTOM: patternId=?, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C493/initial_net.png", "targetTopFaceImage": "images/C493/target_top_face.png"}, "__sample_id__": "C493"} +{"taskType": "roll_to_target_top_face", "code": "C494", "name": "Goal Roll C494", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "S", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "plus", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "T", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "smile", "rotation": 180}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "S", "rotation": 180}, "RIGHT": {"patternId": "plus", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "T", "rotation": 0}, "BOTTOM": {"patternId": "smile", "rotation": 180}}}, "targetTopFace": {"sourceObservationIndex": 7, "stepNumber": 8, "patternId": "T", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C494/initial_net.png", "targetTopFaceImage": "../images/C494/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 8, "targetRotationOffset": 180, "levelId": 494, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-494.json"}, "rollSequence": ["W", "S", "S", "N", "N", "E", "S", "E", "W", "N"], "observedPathFaces": [{"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "T", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "plus", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "S", "S", "N", "N", "E", "S", "E", "W", "N"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "S", "rotation": 180}, "RIGHT": {"patternId": "plus", "rotation": 270}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "T", "rotation": 0}, "BOTTOM": {"patternId": "smile", "rotation": 180}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C494\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=T, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=T, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=plus, rotation=270]\n [FRONT: patternId=S, rotation=180]\n [BOTTOM: patternId=smile, rotation=180]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=T, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=plus, rotation=270\n- FRONT: patternId=S, rotation=180\n- BOTTOM: patternId=smile, rotation=180\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C494/initial_net.png", "targetTopFaceImage": "images/C494/target_top_face.png"}, "__sample_id__": "C494"} +{"taskType": "roll_to_target_top_face", "code": "C495", "name": "Goal Roll C495", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "K", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "S", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "heart", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "X", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "circle", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "R", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "K", "rotation": 270}, "FRONT": {"patternId": "S", "rotation": 90}, "RIGHT": {"patternId": "heart", "rotation": 180}, "BACK": {"patternId": "X", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 0}, "BOTTOM": {"patternId": "R", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 8, "stepNumber": 9, "patternId": "heart", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C495/initial_net.png", "targetTopFaceImage": "../images/C495/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 9, "targetRotationOffset": 90, "levelId": 495, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-495.json"}, "rollSequence": ["N", "N", "S", "W", "S", "S", "N", "W", "N", "W"], "observedPathFaces": [{"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "X", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "R", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "K", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "N", "S", "W", "S", "S", "N", "W", "N", "W"]}, "legacy_answer": {"TOP": {"patternId": "K", "rotation": 270}, "FRONT": {"patternId": "S", "rotation": 90}, "RIGHT": {"patternId": "heart", "rotation": 180}, "BACK": {"patternId": "X", "rotation": 0}, "LEFT": {"patternId": "circle", "rotation": 0}, "BOTTOM": {"patternId": "R", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C495\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=heart, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=X, rotation=0]\n[LEFT: patternId=circle, rotation=0] [TOP: patternId=K, rotation=270] [RIGHT: patternId=heart, rotation=180]\n [FRONT: patternId=S, rotation=90]\n [BOTTOM: patternId=R, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=X, rotation=0\n- LEFT: patternId=circle, rotation=0\n- TOP: patternId=K, rotation=270\n- RIGHT: patternId=heart, rotation=180\n- FRONT: patternId=S, rotation=90\n- BOTTOM: patternId=R, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C495/initial_net.png", "targetTopFaceImage": "images/C495/target_top_face.png"}, "__sample_id__": "C495"} +{"taskType": "roll_to_target_top_face", "code": "C496", "name": "Goal Roll C496", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "Z", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "6", "rotation": 180}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "Z", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "2", "rotation": 90}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "1", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "G", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "Z", "rotation": 0}, "FRONT": {"patternId": "6", "rotation": 180}, "RIGHT": {"patternId": "Z", "rotation": 0}, "BACK": {"patternId": "2", "rotation": 90}, "LEFT": {"patternId": "1", "rotation": 0}, "BOTTOM": {"patternId": "G", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 9, "stepNumber": 10, "patternId": "1", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C496/initial_net.png", "targetTopFaceImage": "../images/C496/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 10, "targetRotationOffset": 270, "levelId": 496, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-496.json"}, "rollSequence": ["E", "S", "S", "N", "N", "E", "N", "E", "N", "N"], "observedPathFaces": [{"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "6", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "S", "N", "N", "E", "N", "E", "N", "N"]}, "legacy_answer": {"TOP": {"patternId": "Z", "rotation": 0}, "FRONT": {"patternId": "6", "rotation": 180}, "RIGHT": {"patternId": "Z", "rotation": 0}, "BACK": {"patternId": "2", "rotation": 90}, "LEFT": {"patternId": "1", "rotation": 0}, "BOTTOM": {"patternId": "G", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C496\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=1, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=2, rotation=90]\n[LEFT: patternId=1, rotation=0] [TOP: patternId=Z, rotation=0] [RIGHT: patternId=Z, rotation=0]\n [FRONT: patternId=6, rotation=180]\n [BOTTOM: patternId=G, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=2, rotation=90\n- LEFT: patternId=1, rotation=0\n- TOP: patternId=Z, rotation=0\n- RIGHT: patternId=Z, rotation=0\n- FRONT: patternId=6, rotation=180\n- BOTTOM: patternId=G, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C496/initial_net.png", "targetTopFaceImage": "images/C496/target_top_face.png"}, "__sample_id__": "C496"} +{"taskType": "roll_to_target_top_face", "code": "C497", "name": "Goal Roll C497", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "3", "rotation": 270}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "Z", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "2", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "F", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "4", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "2", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "3", "rotation": 270}, "FRONT": {"patternId": "Z", "rotation": 0}, "RIGHT": {"patternId": "2", "rotation": 90}, "BACK": {"patternId": "F", "rotation": 180}, "LEFT": {"patternId": "4", "rotation": 270}, "BOTTOM": {"patternId": "2", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 9, "stepNumber": 10, "patternId": "F", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C497/initial_net.png", "targetTopFaceImage": "../images/C497/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 10, "targetRotationOffset": 270, "levelId": 497, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-497.json"}, "rollSequence": ["S", "E", "N", "N", "W", "S", "W", "S", "W", "W"], "observedPathFaces": [{"patternId": "Z", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "3", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "Z", "rotation": 90, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["S", "E", "N", "N", "W", "S", "W", "S", "W", "W"]}, "legacy_answer": {"TOP": {"patternId": "3", "rotation": 270}, "FRONT": {"patternId": "Z", "rotation": 0}, "RIGHT": {"patternId": "2", "rotation": 90}, "BACK": {"patternId": "F", "rotation": 180}, "LEFT": {"patternId": "4", "rotation": 270}, "BOTTOM": {"patternId": "2", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C497\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=F, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=F, rotation=180]\n[LEFT: patternId=4, rotation=270] [TOP: patternId=3, rotation=270] [RIGHT: patternId=2, rotation=90]\n [FRONT: patternId=Z, rotation=0]\n [BOTTOM: patternId=2, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=F, rotation=180\n- LEFT: patternId=4, rotation=270\n- TOP: patternId=3, rotation=270\n- RIGHT: patternId=2, rotation=90\n- FRONT: patternId=Z, rotation=0\n- BOTTOM: patternId=2, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C497/initial_net.png", "targetTopFaceImage": "images/C497/target_top_face.png"}, "__sample_id__": "C497"} +{"taskType": "roll_to_target_top_face", "code": "C498", "name": "Goal Roll C498", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "arrow_left", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "J", "rotation": 270}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "circle", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "heart", "rotation": 180}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "triangle", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_up", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "arrow_left", "rotation": 90}, "FRONT": {"patternId": "J", "rotation": 270}, "RIGHT": {"patternId": "circle", "rotation": 0}, "BACK": {"patternId": "heart", "rotation": 180}, "LEFT": {"patternId": "triangle", "rotation": 90}, "BOTTOM": {"patternId": "arrow_up", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 8, "stepNumber": 9, "patternId": "arrow_left", "rotation": 180}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C498/initial_net.png", "targetTopFaceImage": "../images/C498/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 9, "targetRotationOffset": 180, "levelId": 498, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-498.json"}, "rollSequence": ["E", "S", "S", "S", "W", "E", "E", "S", "S", "N"], "observedPathFaces": [{"patternId": "circle", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "triangle", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "heart", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "circle", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "S", "S", "W", "E", "E", "S", "S", "N"]}, "legacy_answer": {"TOP": {"patternId": "arrow_left", "rotation": 90}, "FRONT": {"patternId": "J", "rotation": 270}, "RIGHT": {"patternId": "circle", "rotation": 0}, "BACK": {"patternId": "heart", "rotation": 180}, "LEFT": {"patternId": "triangle", "rotation": 90}, "BOTTOM": {"patternId": "arrow_up", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C498\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=arrow_left, rotation=180\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=heart, rotation=180]\n[LEFT: patternId=triangle, rotation=90] [TOP: patternId=arrow_left, rotation=90] [RIGHT: patternId=circle, rotation=0]\n [FRONT: patternId=J, rotation=270]\n [BOTTOM: patternId=arrow_up, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=heart, rotation=180\n- LEFT: patternId=triangle, rotation=90\n- TOP: patternId=arrow_left, rotation=90\n- RIGHT: patternId=circle, rotation=0\n- FRONT: patternId=J, rotation=270\n- BOTTOM: patternId=arrow_up, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C498/initial_net.png", "targetTopFaceImage": "images/C498/target_top_face.png"}, "__sample_id__": "C498"} +{"taskType": "roll_to_target_top_face", "code": "C499", "name": "Goal Roll C499", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "S", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "smile", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "2", "rotation": 90}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "4", "rotation": 180}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "square", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "S", "rotation": 90}, "FRONT": {"patternId": "smile", "rotation": 0}, "RIGHT": {"patternId": "2", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "4", "rotation": 180}, "BOTTOM": {"patternId": "square", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "S", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C499/initial_net.png", "targetTopFaceImage": "../images/C499/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 5, "targetRotationOffset": 270, "levelId": 499, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-499.json"}, "rollSequence": ["E", "E", "S", "W", "S", "E", "N", "E", "E", "S"], "observedPathFaces": [{"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "2", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "4", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "E", "S", "W", "S", "E", "N", "E", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "S", "rotation": 90}, "FRONT": {"patternId": "smile", "rotation": 0}, "RIGHT": {"patternId": "2", "rotation": 90}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "4", "rotation": 180}, "BOTTOM": {"patternId": "square", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C499\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=S, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=4, rotation=180] [TOP: patternId=S, rotation=90] [RIGHT: patternId=2, rotation=90]\n [FRONT: patternId=smile, rotation=0]\n [BOTTOM: patternId=square, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=4, rotation=180\n- TOP: patternId=S, rotation=90\n- RIGHT: patternId=2, rotation=90\n- FRONT: patternId=smile, rotation=0\n- BOTTOM: patternId=square, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C499/initial_net.png", "targetTopFaceImage": "images/C499/target_top_face.png"}, "__sample_id__": "C499"} +{"taskType": "roll_to_target_top_face", "code": "C500", "name": "Goal Roll C500", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "smile", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "1", "rotation": 0}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "?", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "arrow_up", "rotation": 0}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "arrow_up", "rotation": 270}]}, "solutionFaces": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "smile", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_up", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}}}, "targetTopFace": {"sourceObservationIndex": 9, "stepNumber": 10, "patternId": "1", "rotation": 270}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C500/initial_net.png", "targetTopFaceImage": "../images/C500/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 10, "targetRotationOffset": 90, "levelId": 500, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-500.json"}, "rollSequence": ["E", "S", "N", "S", "S", "W", "N", "W", "S", "S"], "observedPathFaces": [{"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "smile", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "1", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_up", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["E", "S", "N", "S", "S", "W", "N", "W", "S", "S"]}, "legacy_answer": {"TOP": {"patternId": "?", "rotation": 0}, "FRONT": {"patternId": "smile", "rotation": 0}, "RIGHT": {"patternId": "1", "rotation": 0}, "BACK": {"patternId": "?", "rotation": 0}, "LEFT": {"patternId": "arrow_up", "rotation": 0}, "BOTTOM": {"patternId": "arrow_up", "rotation": 270}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C500\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=1, rotation=270\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=?, rotation=0]\n[LEFT: patternId=arrow_up, rotation=0] [TOP: patternId=?, rotation=0] [RIGHT: patternId=1, rotation=0]\n [FRONT: patternId=smile, rotation=0]\n [BOTTOM: patternId=arrow_up, rotation=270]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=?, rotation=0\n- LEFT: patternId=arrow_up, rotation=0\n- TOP: patternId=?, rotation=0\n- RIGHT: patternId=1, rotation=0\n- FRONT: patternId=smile, rotation=0\n- BOTTOM: patternId=arrow_up, rotation=270\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C500/initial_net.png", "targetTopFaceImage": "images/C500/target_top_face.png"}, "__sample_id__": "C500"} +{"taskType": "roll_to_target_top_face", "code": "C501", "name": "Goal Roll C501", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "W", "rotation": 0}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "arrow_left", "rotation": 0}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_right", "rotation": 180}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "J", "rotation": 0}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "A", "rotation": 90}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "square", "rotation": 0}]}, "solutionFaces": {"TOP": {"patternId": "W", "rotation": 0}, "FRONT": {"patternId": "arrow_left", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 180}, "BACK": {"patternId": "J", "rotation": 0}, "LEFT": {"patternId": "A", "rotation": 90}, "BOTTOM": {"patternId": "square", "rotation": 0}}}, "targetTopFace": {"sourceObservationIndex": 0, "stepNumber": 1, "patternId": "arrow_right", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C501/initial_net.png", "targetTopFaceImage": "../images/C501/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 1, "targetRotationOffset": 270, "levelId": 501, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-501.json"}, "rollSequence": ["W", "W", "W", "S", "S", "W", "W", "N", "E", "E"], "observedPathFaces": [{"patternId": "A", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "W", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 90, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_left", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "square", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "J", "rotation": 270, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["W", "W", "W", "S", "S", "W", "W", "N", "E", "E"]}, "legacy_answer": {"TOP": {"patternId": "W", "rotation": 0}, "FRONT": {"patternId": "arrow_left", "rotation": 0}, "RIGHT": {"patternId": "arrow_right", "rotation": 180}, "BACK": {"patternId": "J", "rotation": 0}, "LEFT": {"patternId": "A", "rotation": 90}, "BOTTOM": {"patternId": "square", "rotation": 0}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C501\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=arrow_right, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=J, rotation=0]\n[LEFT: patternId=A, rotation=90] [TOP: patternId=W, rotation=0] [RIGHT: patternId=arrow_right, rotation=180]\n [FRONT: patternId=arrow_left, rotation=0]\n [BOTTOM: patternId=square, rotation=0]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=J, rotation=0\n- LEFT: patternId=A, rotation=90\n- TOP: patternId=W, rotation=0\n- RIGHT: patternId=arrow_right, rotation=180\n- FRONT: patternId=arrow_left, rotation=0\n- BOTTOM: patternId=square, rotation=0\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C501/initial_net.png", "targetTopFaceImage": "images/C501/target_top_face.png"}, "__sample_id__": "C501"} +{"taskType": "roll_to_target_top_face", "code": "C502", "name": "Goal Roll C502", "description": "Given the initial cross net and the target top-face image, output a roll sequence that moves the cube to the target state.", "instructions": {"en": "You are given the initial state of the cube as a cross-shaped net. This net is the unfolded outer surface of the folded cube. Each visible cell is labeled as TOP, BOTTOM, FRONT, BACK, LEFT, or RIGHT. The number under each visible face is the clockwise rotation in degrees from the original upright pattern. Output a roll sequence so that, at the end, the cube's top face seen from above exactly matches the target image.", "directionVocabulary": {"N": "Up", "S": "Down", "W": "Left", "E": "Right"}}, "initialCube": {"net": {"layout": "reconstruction_cross", "faceOrder": ["TOP", "FRONT", "RIGHT", "BACK", "LEFT", "BOTTOM"], "cells": [{"faceKey": "TOP", "faceLabelZh": "TOP", "row": 1, "col": 1, "patternId": "A", "rotation": 90}, {"faceKey": "FRONT", "faceLabelZh": "FRONT", "row": 2, "col": 1, "patternId": "G", "rotation": 90}, {"faceKey": "RIGHT", "faceLabelZh": "RIGHT", "row": 1, "col": 2, "patternId": "arrow_right", "rotation": 270}, {"faceKey": "BACK", "faceLabelZh": "BACK", "row": 0, "col": 1, "patternId": "F", "rotation": 270}, {"faceKey": "LEFT", "faceLabelZh": "LEFT", "row": 1, "col": 0, "patternId": "S", "rotation": 270}, {"faceKey": "BOTTOM", "faceLabelZh": "BOTTOM", "row": 3, "col": 1, "patternId": "C", "rotation": 90}]}, "solutionFaces": {"TOP": {"patternId": "A", "rotation": 90}, "FRONT": {"patternId": "G", "rotation": 90}, "RIGHT": {"patternId": "arrow_right", "rotation": 270}, "BACK": {"patternId": "F", "rotation": 270}, "LEFT": {"patternId": "S", "rotation": 270}, "BOTTOM": {"patternId": "C", "rotation": 90}}}, "targetTopFace": {"sourceObservationIndex": 4, "stepNumber": 5, "patternId": "A", "rotation": 0}, "answers": {"directions": [], "moveCount": 0, "referenceValid": false}, "imagePaths": {"initialNetImage": "../images/C502/initial_net.png", "targetTopFaceImage": "../images/C502/target_top_face.png"}, "metadata": {"difficulty": 5, "tier": 5, "targetStepNumber": 5, "targetRotationOffset": 180, "levelId": 502, "moveCount": 10, "sourceLevelPath": "levels/reconstruct/generated-502.json"}, "rollSequence": ["N", "E", "N", "E", "E", "W", "S", "E", "E", "S"], "observedPathFaces": [{"patternId": "F", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 180, "flipHorizontal": false, "flipVertical": true}, {"patternId": "A", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "G", "rotation": 0, "flipHorizontal": false, "flipVertical": true}, {"patternId": "arrow_right", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "C", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "S", "rotation": 270, "flipHorizontal": false, "flipVertical": true}, {"patternId": "F", "rotation": 180, "flipHorizontal": false, "flipVertical": true}], "answer": {"directions": ["N", "E", "N", "E", "E", "W", "S", "E", "E", "S"]}, "legacy_answer": {"TOP": {"patternId": "A", "rotation": 90}, "FRONT": {"patternId": "G", "rotation": 90}, "RIGHT": {"patternId": "arrow_right", "rotation": 270}, "BACK": {"patternId": "F", "rotation": 270}, "LEFT": {"patternId": "S", "rotation": 270}, "BOTTOM": {"patternId": "C", "rotation": 90}}, "prompt": {"system": "You are a cube-rolling sequence solver. Given a cube whose initial outer-surface configuration is shown as a cross net and a target top-face image, output one valid sequence of N/S/E/W rolls so that the cube's top face after the sequence matches the target.\n\nYou will receive: (a) one initial cross-net image showing the visible faces of the unfolded cube with their patternIds and rotations, (b) one target top-face image showing the desired final top-face pattern and orientation, and (c) a structured text body listing every visible net cell, the target patternId+rotation, the direction vocabulary, and the maximum allowed sequence length.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: \n\nThe JSON object must follow the directions schema described in section 8 of the user prompt. Multiple sequences may be valid — output any one that solves the puzzle. Do NOT wrap FINAL_JSON in Markdown code fences. Do NOT write anything after the FINAL_JSON line. Emit exactly one FINAL_JSON line.\n\nIf you cannot reason out a confident sequence, still output your best-effort FINAL_JSON line with at least one direction token; the only structurally invalid output is no FINAL_JSON line at all. Never refuse, never return prose only.", "user": "## 1. TASK\nOutput one sequence of rolls so that, at the end of the sequence, the cube's top face seen from above matches the target top face exactly (both patternId and rotation).\nThe puzzle is solved when the engine simulates your sequence on the initial cube and the resulting top-face pattern equals the target.\n\n## 2. WORLD MODEL\n- Cube: a unit cube with one pattern printed on each of its six outer faces. The faces are named TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT in the world frame.\n- Cross net: the unfolded outer surface laid flat. Each cell is one face; its label tells you which face it is and its number under the patternId is the clockwise rotation in degrees from the original upright pattern.\n- Roll: tipping the cube 90° about one of its bottom edges into an adjacent grid cell. After a roll, the face that was on the side becomes the new top, the previous top moves to the opposite side, and so on.\n- Direction tokens: N (roll up / north), S (roll down / south), E (roll right / east), W (roll left / west). The direction is always relative to the world frame, not the cube's current orientation.\n- Target top face: the desired patternId and rotation of whichever face ends up on top after the sequence.\n\n## 3. VISUAL LEGEND\n- Image 1: initial cross-net of the cube. The TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT cells are arranged in a cross. Each visible face shows its patternId and a number indicating the clockwise rotation in degrees from the upright orientation.\n- Image 2: the target top-face image, showing the patternId and rotation the cube's top face must reach.\n- Coordinates: the cube starts at (0, 0). N decrements y (up on screen), S increments y, E increments x (right), W decrements x.\n\n## 4. INPUT FIELDS\n- sample_id: C502\n- task_type: roll_to_target_top_face\n- difficulty: 5\n- target_top_face: patternId=A, rotation=0\n- max_direction_steps: 20\n- initial_net_layout (text view, with the BACK / LEFT-TOP-RIGHT / FRONT / BOTTOM rows of the cross):\n [BACK: patternId=F, rotation=270]\n[LEFT: patternId=S, rotation=270] [TOP: patternId=A, rotation=90] [RIGHT: patternId=arrow_right, rotation=270]\n [FRONT: patternId=G, rotation=90]\n [BOTTOM: patternId=C, rotation=90]\n- initial_net_cells (explicit list of every visible face):\n- BACK: patternId=F, rotation=270\n- LEFT: patternId=S, rotation=270\n- TOP: patternId=A, rotation=90\n- RIGHT: patternId=arrow_right, rotation=270\n- FRONT: patternId=G, rotation=90\n- BOTTOM: patternId=C, rotation=90\n\n## 5. ACTION VOCABULARY\nA complete answer is one ordered list of direction tokens:\n- direction: one of {\"N\", \"S\", \"E\", \"W\"}.\n- Sequence length is the number of rolls. The maximum allowed length for this task is `max_direction_steps`.\n- Multiple sequences may produce the same target top face; any one of them counts as correct.\n\n## 6. CONSTRAINTS\n- Each direction token must be exactly one of N, S, E, W (uppercase).\n- The sequence length must be between 1 and `max_direction_steps` inclusive.\n- The sequence must be deterministic: no probabilistic or \"either-or\" entries. One direction per step.\n- The engine evaluates by simulating your sequence on the initial cube; do not output any other JSON keys.\n\n## 7. SOLVING ADVICE\n- Track which face is currently on top after each roll. A roll N moves the FRONT face to the new TOP, S moves BACK to TOP, E moves LEFT to TOP, W moves RIGHT to TOP (with appropriate rotation).\n- Confirm the rotation of the target top face — getting the patternId right but the rotation wrong is still a fail. Each roll N or S adjusts the cube's local-frame rotation by 0/180; each roll E or W adjusts it by ±90.\n- A reference sequence may be inferable from the imprint history if the data includes one, but you do not need to copy it; output any valid sequence.\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"directions\":[\"\", ...]}\n- directions: array of direction tokens.\n- Each token: one of `\"N\"`, `\"S\"`, `\"E\"`, `\"W\"`.\n- Length: 1..20.\n\n## 9. FINAL INSTRUCTION\nYou may include reasoning above, but the very last line of your reply must start with FINAL_JSON: followed by exactly one valid JSON object.\nDo not wrap FINAL_JSON in code fences and do not write anything after it."}, "images_relative_to_config": {"initialNetImage": "images/C502/initial_net.png", "targetTopFaceImage": "images/C502/target_top_face.png"}, "__sample_id__": "C502"}